This page provides a list of all articles available at PlanetMath in the following topic:
- 20-XX Group theory and generalizations.
This list will be periodically updated. Each entry in the list has three fields:
- PM : The first field is the link to the PlanetMath article, along with the article's object ID.
- WP : The second field is either a "guessed" link to a correspondingly named Wikipedia article, produced by the script which generated the list, or one or more manually entered links to the corresponding Wikipedia articles on the subject.
- Status : The third field is the status field, which explains the current status of the entry. The recommended status entries are:
| Status | means PM article |
| N | not needed |
| A | adequately covered |
| C | copied |
| M | merged |
| NC | needs copying |
| NM | needs merging |
- Please update the WP and Status fields as appropriate.
- if the WP field is correct please remove the qualifier "guess".
- If the corresponding Wikipedia article exists, but the link to it is wrong, please fix the link.
- If you copy or merge an article from PlanetMath, please update the WP and Status fields for that entry.
- If you have any comments, for example, thoughts on how the PlanetMath article compares to the corresponding Wikipedia article(s), please place such comments on a new indented line following the entry. Comments of this kind are very valuable.
Don't forget to include the relevant template if you copy over text or feel like an external link is warranted
- {{planetmath|id=|title=}} for copied over text
- {{planetmath reference|id=|title=}} for an external link
See the main page for examples and usage criteria.
One can use the web-based program Pmform to convert PlanetMath articles to the Wikipedia format. As a side benefit, this tool will place the PlanetMath template for you.
- PM: alternating group is a normal subgroup of the symmetric group, id=4387 -- WP: symmetric group -- Status: A
- PM: associative, id=2150 -- WP: associative -- Status: A
- PM: bibliography for group theory, id=5683 -- WP: List of publications in mathematics#Group theory -- Status: NM
- PM: canonical projection, id=3950 -- WP: quotient group -- Status: A
- PM: centralizer, id=2833 -- WP: centralizer -- Status: A
- PM: commutative, id=2148 -- WP: commutative -- Status: A
- PM: examples of groups, id=3144 -- WP: examples of groups -- Status: NM
- PM: general associativity, id=6165 -- WP: general associativity -- Status: N
- PM: group, id=78 -- WP: group (mathematics) -- Status: A
- PM: groups of small order, id=6451 -- WP: examples of groups -- Status: NM
- PM: inverse forming in proportion to group operation, id=6575 -- WP guess: group (mathematics) -- Status: A
- PM: quotient group, id=1127 -- WP: quotient group -- Status: A
- PM: uniqueness of inverse (for groups), id=5687 -- WP guess: group (mathematics) -- Status: A
- PM: correspondence of normal subgroups and group congruences, id=7445 -- WP guess: correspondence of normal subgroups and group congruences -- Status:
- PM: cube of a number, id=6859 -- WP guess: cube of a number -- Status:
- PM: examples of non-commutative operations, id=6768 -- WP: Commutative operation -- Status: A
- PM: indecomposable group, id=7232 -- WP guess: indecomposable group -- Status:
- PM: proof that a subgroup of a group defines an equivalence relation on the group, id=7443 -- WP guess: proof that a subgroup of a group defines an equivalence relation on the group -- Status:
- PM: the alternating group has index 2 in the symmetric group, id=9048new! -- WP guess: the alternating group has index 2 in the symmetric group -- Status:
- PM: Bruhat decomposition, id=7669new! -- WP guess: Bruhat decomposition -- Status:
- PM: length function, id=4365 -- WP: length function -- Status: C
- PM: a characterization of groups, id=6391 -- WP: semigroup -- Status: NM
- PM: center, id=2191 -- WP: center of a group -- Status: A
- PM: characteristic subgroup, id=3180 -- WP: characteristic subgroup -- Status: A
- PM: class function, id=1847 -- WP: class function -- Status: A
- PM: conjugacy class, id=1848 -- WP: conjugacy class -- Status: A
- PM: conjugacy class formula, id=3624 -- WP: conjugacy class -- Status: A
- PM: conjugate stabilizer subgroups, id=3888 -- WP guess: conjugate stabilizer subgroups -- Status:
- PM: cyclic group, id=2185 -- WP: cyclic group -- Status: A
- PM: derived subgroup, id=2812 -- WP: derived subgroup -- Status: A
- PM: equivariant, id=4709 -- WP: equivariant -- Status: A
- PM: examples of finite simple groups, id=3568 -- WP: list of finite simple groups -- Status: A
- PM: Feit-Thompson theorem, id=4503 -- WP: Feit-Thompson theorem -- Status: A
- PM: finitely generated group, id=1726 -- WP: finitely generated group -- Status: A
- PM: fourth isomorphism theorem, id=4917 -- WP: isomorphism theorem -- Status: A
- PM: generator, id=4094 -- WP: generating set of a group -- Status: A
- PM: group actions and homomorphisms, id=3820 -- WP: group action -- Status: NM
- PM: group homomorphism, id=719 -- WP: group homomorphism -- Status: A
- PM: homogeneous space, id=4038 -- WP: group action -- Status: A
- PM: identity element, id=3140 -- WP: identity element -- Status: A
- PM: inner automorphism, id=3155 -- WP: inner automorphism -- Status: A
- PM: isomorphic groups, id=5127 -- WP: group (mathematics) -- Status: A
- PM: kernel, id=812 -- WP: group homomorphism -- Status: A
- PM: maximal, id=2198 -- WP: maximal subgroup -- Status: A
- PM: normal closure, id=6307 -- WP: normal closure -- Status: A
- PM: normal subgroup, id=1305 -- WP: normal subgroup -- Status: A
- PM: normality of subgroups is not transitive, id=3147 -- WP: normal subgroup -- Status: A
- PM: normalizer, id=2873 -- WP: normalizer -- Status: A
- PM: order (of a group), id=2871 -- WP guess: Group (mathematics) -- Status: A
- PM: presentation of a group, id=2182 -- WP guess: presentation of a group -- Status: A
- PM: proof of first isomorphism theorem, id=2922 -- WP guess: isomorphism theorem -- Status: N
- I've put an external link to PM proof AdamSmithee 09:09, 12 January 2006 (UTC)
- PM: proof of fourth isomorphism theorem, id=5749 -- WP guess: proof of fourth isomorphism theorem -- Status:
- PM: proof of second isomorphism theorem, id=3153 -- WP guess: isomorphism theorem -- Status: N
- I've put an external link to PM proof AdamSmithee 09:09, 12 January 2006 (UTC)
- PM: proof that all cyclic groups are abelian, id=4096 -- WP guess: proof that all cyclic groups are abelian -- Status:
- PM: proof that all cyclic groups of the same order are isomorphic to each other, id=4095 -- WP guess: proof that all cyclic groups of the same order are isomorphic to each other -- Status:
- PM: proof that all subgroups of a cyclic group are cyclic, id=4097 -- WP guess: proof that all subgroups of a cyclic group are cyclic -- Status:
- PM: Proof: The orbit of any element of a group is a subgroup, id=4102 -- WP guess: Proof: The orbit of any element of a group is a subgroup -- Status:
- PM: regular group action, id=3884 -- WP: regular group action -- Status: A
- PM: simple group, id=2189 -- WP: simple group -- Status: A
- PM: solvable group, id=1336 -- WP: solvable group -- Status: A
- PM: a subgroup of index 2 is normal, id=6905 -- WP guess: a subgroup of index 2 is normal -- Status:
- PM: core of a subgroup, id=7547 -- WP guess: core of a subgroup -- Status:
- PM: Fundamental homomorphism theorem, id=7495 -- WP guess: Fundamental homomorphism theorem -- Status:
- PM: generating set of a group, id=7545 -- WP guess: generating set of a group -- Status:
- PM: nonabelian group, id=5138 -- WP: nonabelian group -- Status:A
- PM: proof of third isomorphism theorem, id=7496 -- WP: isomorphism theorem -- Status: N
- I added an external link to the proof AdamSmithee 08:51, 7 March 2006 (UTC)
- PM: a group of even order contains an element of order 2, id=9512new! -- WP guess: a group of even order contains an element of order 2 -- Status:
- PM: double coset, id=8408new! -- WP guess: double coset -- Status:
- PM: groups with abelian inner automorphism group, id=9799new! -- WP guess: groups with abelian inner automorphism group -- Status:
- PM: homogeneous group, id=8298new! -- WP guess: homogeneous group -- Status:
- PM: normality of subgroups of prime index, id=9825new! -- WP guess: normality of subgroups of prime index -- Status:
- PM: one-sided normality of subsemigroup, id=8265new! -- WP guess: one-sided normality of subsemigroup -- Status:
- PM: order of elements in finite groups, id=8757new! -- WP guess: order of elements in finite groups -- Status:
- PM: the derived subgroup is normal, id=8135new! -- WP guess: the derived subgroup is normal -- Status:
- PM: the kernel of a group homomorphism is a normal subgroup, id=9698new! -- WP guess: the kernel of a group homomorphism is a normal subgroup -- Status:
- PM: Cayley table, id=3540 -- WP: Cayley table -- Status: A
- PM: direct product and restricted direct product of groups, id=6560 -- WP: direct product, direct sum-- Status: NM
- Some work needs to be done here to draw the distinctions between direct sum and direct product. Merging together the two articles might be a good idea. Jtwdog 17:50, 26 October 2005 (UTC)
- PM: proper subgroup, id=3141 -- WP: proper subgroup -- Status: A
- PM: quaternion group, id=2844 -- WP: quaternion group -- Status: A
- PM: generalized quaternion group, id=8620new! -- WP guess: generalized quaternion group -- Status:
- PM: proof that G is cyclic if and only if \lvert G \rvert=\exp(G), id=8759new! -- WP guess: proof that G is cyclic if and only if \lvert G \rvert=\exp(G) -- Status:
- PM: proof that a finite abelian group has element with \lvert g\rvert=\exp(G), id=8758new! -- WP guess: proof that a finite abelian group has element with \lvert g\rvert=\exp(G) -- Status:
- PM: permutation group, id=3758 -- WP: permutation group -- Status: A
- PM: blocks of permutation groups, id=9668new! -- WP guess: blocks of permutation groups -- Status:
- PM: conjugacy classes in the symmetric group S_n, id=9613new! -- WP guess: conjugacy classes in the symmetric group S_n -- Status:
- PM: primitive permutation group, id=4913 -- WP: primitive permutation group -- Status: A
- PM: doubly transitive groups are primitive, id=9724new! -- WP guess: doubly transitive groups are primitive -- Status:
- PM: examples of primitive groups that are not doubly transitive, id=9742new! -- WP guess: examples of primitive groups that are not doubly transitive -- Status:
- PM: transitive actions are primitive if and only if stabilizers are maximal subgroups, id=9669new! -- WP guess: transitive actions are primitive if and only if stabilizers are maximal subgroups -- Status:
- PM: Jordan's theorem (multiply transitive groups), id=3761 -- WP: Mathieu group -- Status: M
- PM: multiply transitive, id=3759 -- WP: multiply transitive -- Status: M
- PM: sharply multiply transitive, id=3760 -- WP: sharply multiply transitive -- Status: M
- PM: alternative characterization of multiply transitive permutation groups, id=9723new! -- WP guess: alternative characterization of multiply transitive permutation groups -- Status:
- PM: example of multiply transitive, id=9726new! -- WP guess: example of multiply transitive -- Status:
- PM: symmetric group, id=5421 -- WP: symmetric group -- Status: A
- PM: symmetric group, id=1040 -- WP: symmetric group -- Status:A
- PM: symmetric group is generated by adjacent transpositions, id=9054new! -- WP guess: symmetric group is generated by adjacent transpositions -- Status:
- PM: symmetric group on three letters, id=7870new! -- WP guess: symmetric group on three letters -- Status:
- PM: two isomorphic groups, id=7871new! -- WP guess: two isomorphic groups -- Status:
- PM: Cayley's theorem, id=2174 -- WP: permutation group -- Status: A
- PM: finding the order of a group, id=7904new! -- WP guess: finding the order of a group -- Status:
- PM: Frobenius group, id=3757 -- WP: Frobenius group -- Status: A
- PM: proof of Cayley's theorem, id=2751 -- WP guess: proof of Cayley's theorem -- Status:N
- PM: permutation group on a set, id=5022 -- WP guess: permutation group on a set -- Status:
- PM: a representation which is not completely reducible, id=4122 -- WP: Maschke's theorem -- Status: NM
- It's nice to include counter-examples, though this is probably a low priority. Jtwdog 20:26, 26 October 2005 (UTC)
- PM: Maschke's theorem, id=3874 -- WP: Maschke's theorem -- Status: A
- PM: orthogonality relations, id=3878 -- WP: orthogonality relations -- Status: A
- It would be nice to bring over a little of the proof, as I think it's quite beautiful, but I'll leave that to other's judgement. Jtwdog 20:26, 26 October 2005 (UTC)
- PM: Schur's lemma, id=3570 -- WP: Schur's lemma -- Status: A
- PM: example of immanent, id=5479 -- WP guess: example of immanent -- Status:
- PM: unitary representation, id=9111new! -- WP guess: unitary representation -- Status:
- PM: G-module, id=6663 -- WP: group algebra -- Status: A
- PM: character, id=1843 -- WP: character theory -- Status: A
- PM: example of induced representation, id=6160 -- WP guess: example of induced representation -- Status: N
- PM: example of matrix representations, id=6573 -- WP guess: example of matrix representations -- Status: N
- PM: Frobenius reciprocity, id=1842 -- WP: Frobenius reciprocity -- Status: A
- PM: group representation, id=1596 -- WP: group representation -- Status: A
- PM: induced representation, id=1823 -- WP: induced representation -- Status: A
- PM: matrix representation, id=6581 -- WP: group representation -- Status: A
- PM: regular representation, id=1828 -- WP: regular representation -- Status: A
- PM: restriction representation, id=1822 -- WP: restricted representation -- Status: A
- PM: irreducible representations of S_n, id=9566new! -- WP guess: irreducible representations of S_n -- Status:
- PM: proof that dimension of complex irreducible representation divides order of group, id=9460new! -- WP guess: proof that dimension of complex irreducible representation divides order of group -- Status:
- PM: quotient representations, id=8834new! -- WP guess: quotient representations -- Status:
- PM: Burnside p-q theorem, id=3747 -- WP guess: Burnside p-q theorem -- Status:
- PM: classification of semisimple groups, id=3772 -- WP guess: classification of semisimple groups -- Status:
- PM: semisimple group, id=3771 -- WP guess: semisimple group -- Status: A
- PM: Burnside's Theorem, id=8839new! -- WP guess: Burnside's Theorem -- Status:
- PM: simplicity of the alternating groups, id=3569 -- WP guess: simplicity of the alternating groups -- Status:N
- Jtwdog 04:09, 28 October 2005 (UTC)
- Its a proof; added ref to simple group. linas 23:03, 6 April 2007 (UTC)
- PM: example of infinite simple group, id=9148new! -- WP guess: example of infinite simple group -- Status:
- PM: Janko groups, id=4762 -- WP: list of finite simple groups -- Status: A
- PM: supersolvable group, id=4751 -- WP guess: supersolvable group -- Status:
- PM: Čuhinin's theorem, id=3798 -- WP guess: Čuhinin's theorem -- Status:
- PM: Wielandt-Kegel theorem, id=8412new! -- WP guess: Wielandt-Kegel theorem -- Status:
- PM: Burnside basis theorem, id=3750 -- WP guess: Burnside basis theorem -- Status:
- PM: classification of finite nilpotent groups, id=3755 -- WP guess: classification of finite nilpotent groups -- Status:
- PM: finite nilpotent groups, id=7735new! -- WP guess: finite nilpotent groups -- Status:
- PM: Frattini subset, id=8693new! -- WP guess: Frattini subset -- Status:
- PM: proof of the Burnside basis theorem, id=7731new! -- WP guess: proof of the Burnside basis theorem -- Status:
- PM: p-subgroup, id=5184 -- WP guess: p-subgroup -- Status:
- PM: \pi-groups and \pi'-groups, id=3797 -- WP guess: \pi-groups and \pi'-groups -- Status:
- PM: a nontrivial normal subgroup of a finite p-group G and the center of G have nontrivial intersection, id=5827 -- WP guess: a nontrivial normal subgroup of a finite p-group G and the center of G have nontrivial intersection -- Status:
- PM: Burnside normal complement theorem, id=3754 -- WP guess: Burnside normal complement theorem -- Status:
- PM: class equation theorem, id=5821 -- WP guess: class equation theorem -- Status:
- PM: example of groups of order pq, id=6526 -- WP guess: example of groups of order pq -- Status:
- PM: Frattini argument, id=3748 -- WP guess: Frattini argument -- Status:
- PM: groups of order pq, id=3183 -- WP guess: groups of order pq -- Status:
- PM: p-primary component, id=4610 -- WP guess: p-primary component -- Status:
- PM: proof of class equation theorem, id=5823 -- WP guess: proof of class equation theorem -- Status:
- PM: proof of Frattini argument, id=3749 -- WP guess: proof of Frattini argument -- Status:
- PM: proof of Sylow theorems, id=3182 -- WP guess: proof of Sylow theorems -- Status:
- PM: proof that a nontrivial normal subgroup of a finite p-group G and the center of G have nontrivial intersection, id=5828 -- WP guess: proof that a nontrivial normal subgroup of a finite p-group G and the center of G have nontrivial intersection -- Status:
- PM: subgroups containing the normalizers of Sylow subgroups normalize themselves, id=3763 -- WP guess: subgroups containing the normalizers of Sylow subgroups normalize themselves -- Status:
- PM: Sylow p-subgroups, id=5135 -- WP guess: Sylow p-subgroups -- Status:
- PM: Sylow p-subgroup, id=3181 -- WP guess: Sylow p-subgroup -- Status:
- PM: Sylow theorems, id=2243 -- WP guess: Sylow theorems -- Status:
- PM: Sylow's first theorem, id=4910 -- WP guess: Sylow's first theorem -- Status:
- PM: Sylow's third theorem, id=4899 -- WP guess: Sylow's third theorem -- Status:
- PM: characteristically simple group, id=3767 -- WP guess: characteristically simple group -- Status:
- PM: Fitting's theorem, id=4600 -- WP guess: Fitting's theorem -- Status:
- PM: the Frattini subgroup of a finite group is nilpotent, id=3762 -- WP guess: the Frattini subgroup of a finite group is nilpotent -- Status:
- PM: maximal condition, id=4752 -- WP guess: maximal condition -- Status:
- PM: minimal condition, id=4753 -- WP guess: minimal condition -- Status:
- PM: subnormal series, id=4750 -- WP guess: subnormal series -- Status:
- PM: subnormal subgroup, id=3756 -- WP: subnormal subgroup -- Status: A
- PM: Order Conjecture for non-commuting graph of a group, id=7119 -- WP guess: Order Conjecture for non-commuting graph of a group -- Status:
- PM: Cauchy's theorem, id=1569 -- WP: Cauchy's theorem (group theory) -- Status: C
- The ling is currently redirecting to Order (group theory), which mentions the theorem in passing (anyway, the article should be cleaned up). I think that something more like Lagrange's theorem (group theory) would be more appropriate AdamSmithee 09:28, 12 January 2006 (UTC)
- Done AdamSmithee 09:26, 7 March 2006 (UTC)
- PM: exponent, id=4087 -- WP: exponent (group theory) -- Status: A
- PM: fully invariant subgroup, id=3684 -- WP guess: fully invariant subgroup -- Status:
- PM: Lagrange's theorem, id=1566 -- WP: Lagrange's theorem (group theory) -- Status: A
- PM: proof of Cauchy's theorem, id=2186 -- WP: Cauchy's theorem (group theory) -- Status: N
- NM after creation of the WP article - see above AdamSmithee 09:28, 12 January 2006 (UTC)
- Actually, on a second thought, this is not a particularly illuminating proof. I linked to it AdamSmithee 09:26, 7 March 2006 (UTC)
- PM: proof of Cauchy's theorem in abelian case, id=6045 -- WP guess: proof of Cauchy's theorem in abelian case -- Status:
- PM: proof of Lagrange's theorem, id=1663 -- WP: Lagrange's theorem (group theory) -- Status: A
- PM: proof of the converse of Lagrange's theorem for finite cyclic groups, id=4089 -- WP guess: proof of the converse of Lagrange's theorem for finite cyclic groups -- Status:
- PM: proof that \operatorname{exp}~G divides |G|, id=4091 -- WP guess: G| -- Status:
- PM: proof that |g| divides \operatorname{exp}~G, id=4092 -- WP guess: g| divides \operatornameexp~G -- Status:
- PM: proof that every group of prime order is cyclic, id=4101 -- WP guess: proof that every group of prime order is cyclic -- Status:
- PM: calculus of subgroup orders, id=7766new! -- WP guess: calculus of subgroup orders -- Status:
- PM: example of a non-fully invariant subgroup, id=8172new! -- WP guess: example of a non-fully invariant subgroup -- Status:
- PM: example of fully invariant subgroup, id=8136new! -- WP guess: example of fully invariant subgroup -- Status:
- PM: free group, id=2687 -- WP guess: free group -- Status:
- PM: Nielsen-Schreier theorem, id=3251 -- WP guess: Nielsen-Schreier theorem -- Status:
- PM: proof of Nielsen-Schreier theorem and Schreier index formula, id=4693 -- WP guess: proof of Nielsen-Schreier theorem and Schreier index formula -- Status:
- PM: Schreier index formula, id=4699 -- WP guess: Schreier index formula -- Status:
- PM: reduced word, id=8289new! -- WP guess: reduced word -- Status:
20E06 Free products, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations
- PM: free product, id=6574 -- WP: free product -- Status: NM
- PM: free product with amalgamated subgroup, id=3944 -- WP: free product with amalgamated subgroup -- Status: NM
- PM: HNN extension, id=8122new! -- WP guess: HNN extension -- Status:
- PM: A finitely generated group has only finitely many subgroups of a given index, id=7054 -- WP guess: A finitely generated group has only finitely many subgroups of a given index -- Status:
- PM: Zeta function of a group, id=7053 -- WP guess: Zeta function of a group -- Status:
- PM: example of non-permutable subgroup, id=8375new! -- WP guess: example of non-permutable subgroup -- Status:
- PM: permutable subgroup, id=8372new! -- WP guess: permutable subgroup -- Status:
- PM: metabelian group, id=7532 -- WP guess: metabelian group -- Status:
- PM: example of a Jordan-Hölder decomposition, id=5911 -- WP guess: example of a Jordan-Hölder decomposition -- Status:
- PM: Jordan-Hölder decomposition, id=1332 -- WP guess: Jordan-Hölder decomposition -- Status:
- PM: Schreier refinement theorem, id=6286 -- WP guess: Schreier refinement theorem -- Status:
- PM: ascending series, id=8353new! -- WP guess: ascending series -- Status:
- PM: descending series, id=8352new! -- WP guess: descending series -- Status:
- PM: lattice of subgroups, id=7756new! -- WP guess: lattice of subgroups -- Status:
- PM: normal subgroups form sublattice of a subgroup lattice, id=7770new! -- WP guess: normal subgroups form sublattice of a subgroup lattice -- Status:
- PM: profinite group, id=3134 -- WP: profinite group -- Status: A
- PM: A groups embeds into its profinite completion if and only if it is residually finite, id=7052 -- WP guess: A groups embeds into its profinite completion if and only if it is residually finite -- Status:
- PM: order of a profinite group, id=7228 -- WP guess: order of a profinite group -- Status:
- PM: pro-p group, id=6900 -- WP guess: pro-p group -- Status:
- PM: procyclic group, id=6901 -- WP guess: procyclic group -- Status:
- PM: Profinite completion, id=7051 -- WP guess: Profinite completion -- Status:
- PM: supernatural number, id=7227 -- WP guess: supernatural number -- Status:
- PM: generalized dihedral group, id=6572 -- WP guess: generalized dihedral group -- Status:
- PM: proof of the Jordan Holder decomposition theorem, id=1335 -- WP guess: proof of the Jordan Holder decomposition theorem -- Status:
- PM: semidirect product of groups, id=2829 -- WP guess: semidirect product of groups -- Status:
- PM: wreath product, id=3505 -- WP guess: wreath product -- Status:
- PM: semi-direct factor and quotient group, id=6924 -- WP guess: semi-direct factor and quotient group -- Status:
- PM: examples of semidirect products of groups, id=9747new! -- WP guess: examples of semidirect products of groups -- Status:
- PM: holomorph of a group, id=9746new! -- WP guess: holomorph of a group -- Status:
- PM: virtually cyclic group, id=7746new! -- WP guess: virtually cyclic group -- Status:
- PM: locally \cal P, id=5782 -- WP guess: locally \cal P -- Status:
- PM: locally cyclic group, id=4497 -- WP: locally cyclic group -- Status: A
- PM: subgoups of locally cyclic groups are locally cyclic, id=9577new! -- WP guess: subgoups of locally cyclic groups are locally cyclic -- Status:
- PM: residually \cal P, id=6570 -- WP guess: residually \cal P -- Status:
- PM: subdirect product of groups, id=6571 -- WP guess: subdirect product of groups -- Status:
- PM: existence of maximal subgroups, id=8564new! -- WP guess: existence of maximal subgroups -- Status:
- PM: Jordan-Hölder decomposition theorem, id=1333 -- WP guess: Jordan-Hölder decomposition theorem -- Status:
- PM: homomorphisms of simple groups, id=7644new! -- WP guess: homomorphisms of simple groups -- Status:
- PM: property of infinite simple group, id=8213new! -- WP guess: property of infinite simple group -- Status:
- PM: abelian groups of order 120, id=4654 -- WP guess: abelian groups of order 120 -- Status:
- PM: fundamental theorem of finitely generated abelian groups, id=4652 -- WP guess: fundamental theorem of finitely generated abelian groups -- Status:
- PM: group socle, id=7925new! -- WP guess: group socle -- Status:
- PM: complete group, id=7186 -- WP guess: complete group -- Status:
- PM: conjugacy class, id=5042 -- WP: conjugacy class -- Status: A
- PM: Frattini subgroup, id=2192 -- WP: Frattini subgroup -- Status: A
- PM: non-generator, id=2196 -- WP: non-generator -- Status: A
- PM: abnormal subgroup, id=8635new! -- WP guess: abnormal subgroup -- Status:
- PM: pronormal subgroup, id=8634new! -- WP guess: pronormal subgroup -- Status:
- PM: virtually abelian group, id=6168new! -- WP guess: virtually abelian group -- Status:
- PM: triangle groups, id=5925 -- WP guess: triangle groups -- Status:
- PM: Baumslag-Solitar group, id=9794new! -- WP guess: Baumslag-Solitar group -- Status:
- PM: hyperbolic metric space, id=9509new! -- WP guess: hyperbolic metric space -- Status:
- PM: automatic group, id=5735 -- WP guess: automatic group -- Status:
- PM: Tietze transform, id=7658new! -- WP guess: Tietze transform -- Status:
- PM: properties of group commutators and commutator subgroups, id=7381 -- WP guess: properties of group commutators and commutator subgroups -- Status:
- PM: abelianization, id=6561 -- WP guess: abelianization -- Status:
- PM: transfinite derived series, id=5727 -- WP guess: transfinite derived series -- Status:
- PM: polycyclic group, id=6285 -- WP guess: polycyclic group -- Status:
- PM: metacyclic group, id=7531 -- WP guess: metacyclic group -- Status:
- PM: nilpotent group, id=3113 -- WP: nilpotent group -- Status: A
- PM: Hamiltonian group, id=7520 -- WP guess: Hamiltonian group -- Status:
- PM: enumerating groups, id=7849new! -- WP guess: enumerating groups -- Status:
- PM: locally nilpotent group, id=7619 -- WP guess: locally nilpotent group -- Status:
- PM: normalizer condition, id=8348new! -- WP guess: normalizer condition -- Status:
- PM: inverse limit, id=4655 -- WP: inverse limit -- Status: NM
- PM: outer automorphism group, id=4993 -- WP guess: outer automorphism group -- Status:
- PM: examples of outer automorphism group, id=8682new! -- WP guess: examples of outer automorphism group -- Status:
- PM: braid group, id=4604 -- WP: braid group -- Status: A
- PM: elementary abelian group, id=6566 -- WP guess: elementary abelian group -- Status:
- PM: locally finite group, id=5776 -- WP guess: locally finite group -- Status:
- PM: proof that local finiteness is closed under extension, id=7538 -- WP guess: proof that local finiteness is closed under extension -- Status:
- PM: periodic group, id=7511 -- WP guess: periodic group -- Status:
- PM: quasicyclic group, id=7500 -- WP guess: quasicyclic group -- Status:
- PM: Chernikov group, id=7769new! -- WP guess: Chernikov group -- Status:
- PM: Tarski group, id=7722new! -- WP guess: Tarski group -- Status:
- PM: dihedral group, id=2159 -- WP: dihedral group -- Status: A
- PM: octic group, id=6453 -- WP: dihedral group -- Status: A
- PM: Coxeter group, id=7570 -- WP guess: Coxeter group -- Status:
- PM: dihedral group properties, id=8175new! -- WP guess: dihedral group properties -- Status:
- PM: groups that act freely on trees are free, id=4656 -- WP guess: groups that act freely on trees are free -- Status:
- PM: graph product of groups, id=8263new! -- WP guess: graph product of groups -- Status:
- PM: ping-pong lemma, id=9507new! -- WP guess: ping-pong lemma -- Status:
- PM: perfect group, id=4701 -- WP: perfect group -- Status: A
- PM: essential subgroup, id=7387 -- WP guess: essential subgroup -- Status:
- PM: Hopfian group, id=7516 -- WP guess: Hopfian group -- Status:
- PM: section of a group, id=9584new! -- WP guess: section of a group -- Status:
- PM: computation of the order of GL(n, F_q), id=3541 -- WP guess: computation of the order of GL(n, F_q) -- Status:
- PM: general linear group, id=2462 -- WP guess: general linear group -- Status:
- PM: Nagao's theorem, id=4747 -- WP guess: Nagao's theorem -- Status:
- PM: special linear group, id=2463 -- WP guess: special linear group -- Status:
- PM: theorems of general linear group over a finite field, id=3529 -- WP guess: theorems of general linear group over a finite field -- Status:
- PM: theorems of special linear group over a finite field, id=6620 -- WP guess: theorems of special linear group over a finite field -- Status:
- PM: \mathit{SL}(2,\mathbb{F}_p) has no 1 dimensional irreducible representations over \mathbb{F}_p, id=6915 -- WP guess: \mathitSL(2,\mathbbF_p) has no 1 dimensional irreducible representations over \mathbbF_p -- Status:
- PM: irreducible representations of the special linear group over \mathbb{F}_p, id=6914 -- WP guess: irreducible representations of the special linear group over \mathbbF_p -- Status:
- PM: projective special linear group, id=6912 -- WP guess: projective special linear group -- Status:
- PM: GL_2(\mathbb{Z}), id=8707new! -- WP guess: GL_2(\mathbbZ) -- Status:
- PM: orthogonal group, id=2482 -- WP: orthogonal group -- Status: A
- PM: Ihara's theorem, id=4657 -- WP guess: Ihara's theorem -- Status:
- PM: \mathit{SL}_2(F_3), id=4873 -- WP guess: \mathitSL_2(F_3) -- Status:
- PM: group extension, id=7246 -- WP guess: group extension -- Status:
- PM: factor system, id=5887 -- WP guess: group cohomology -- Status: A
- PM: group cohomology, id=4571 -- WP guess: group cohomology -- Status: A
- PM: stronger Hilbert theorem 90, id=4577 -- WP guess: Hilbert's theorem 90 -- Status: NM
- PM: variety of groups, id=3662 -- WP guess: variety of groups -- Status:
- PM: Schinzel's theorem, id=1115 -- WP guess: Schinzel's theorem -- Status:
- PM: Baer-Specker group, id=7344 -- WP guess: Baer-Specker group -- Status:
- PM: direct product of groups, id=2180 -- WP guess: direct product of groups -- Status:
- PM: example of Schreier's Lemma, id=7903new! -- WP guess: example of Schreier's Lemma -- Status:
- PM: Schreier's lemma, id=7901new! -- WP guess: Schreier's lemma -- Status:
- PM: transversals / lifts / sifts, id=7900new! -- WP guess: transversals / lifts / sifts -- Status:
- PM: divisible closure, id=7993new! -- WP guess: divisible closure -- Status:
- PM: divisible group, id=4499 -- WP: divisible group -- Status: A
- PM: example of divisible group, id=4500 -- WP: divisible group -- Status: N
- PM: Klein 4-group, id=3139 -- WP: Klein 4-group -- Status: A
- PM: abelian group, id=5107 -- WP guess: abelian group -- Status:
- PM: n-divisible group, id=9841new! -- WP guess: n-divisible group -- Status:
- PM: example of Munn tree, id=8294new! -- WP guess: example of Munn tree -- Status:
- PM: free semigroup, id=8287new! -- WP guess: free semigroup -- Status:
- PM: prefix set, id=8292new! -- WP guess: prefix set -- Status:
- PM: presentation of inverse monoids and inverse semigroups, id=8271new! -- WP guess: presentation of inverse monoids and inverse semigroups -- Status:
- PM: Schützenberger graph, id=8268new! -- WP guess: Schützenberger graph -- Status:
- PM: Wagner congruence, id=8272new! -- WP guess: Wagner congruence -- Status:
- PM: word problem, id=8301new! -- WP guess: word problem -- Status:
- PM: existence of maximal semilattice decomposition, id=3553 -- WP guess: existence of maximal semilattice decomposition -- Status:
- PM: Rees factor, id=3517 -- WP guess: Rees factor -- Status:
- PM: semilattice decomposition of a semigroup, id=3552 -- WP guess: semilattice decomposition of a semigroup -- Status:
- PM: simple semigroup, id=3521 -- WP guess: simple semigroup -- Status:
- PM: cancellative semigroup, id=5926 -- WP guess: cancellative semigroup -- Status:
- PM: completely simple semigroup, id=6153new! -- WP guess: completely simple semigroup -- Status:
- PM: free semigroup with involution, id=8283new! -- WP guess: free semigroup with involution -- Status:
- PM: I-semigroup, id=8282new! -- WP guess: I-semigroup -- Status:
- PM: semigroup with involution, id=8281new! -- WP guess: semigroup with involution -- Status:
- PM: Archimedean semigroup, id=3572 -- WP guess: Archimedean semigroup -- Status:
- PM: commutative semigroup, id=3573 -- WP guess: commutative semigroup -- Status:
- PM: regular semigroup, id=5883 -- WP guess: regular semigroup -- Status:
- PM: McAlister covering theorem, id=6201 -- WP guess: McAlister covering theorem -- Status:
- PM: symmetric inverse semigroup, id=8274new! -- WP guess: symmetric inverse semigroup -- Status:
- PM: Wagner-Preston representation theorem, id=8275new! -- WP guess: Wagner-Preston representation theorem -- Status:
- PM: semigroup of transformations, id=3561 -- WP guess: semigroup of transformations -- Status:
- PM: counting theorem, id=2127 -- WP: group action -- Status: A
- PM: example of counting theorem, id=5957 -- WP: group action -- Status: N
- PM: orbit, id=1517 -- WP: group action -- Status: A
- PM: orbit-stabilizer theorem, id=2173 -- WP: group action -- Status: A
- PM: proof of counting theorem, id=3099 -- WP: group action -- Status: N
- PM: proof of orbit-stabilizer theorem, id=2315 -- WP: group action -- Status: N
- PM: simply transitive, id=6208 -- WP: simply transitive -- Status: A
- PM: centralizer of a k-cycle, id=9647new! -- WP guess: centralizer of a k-cycle -- Status:
- PM: conjugacy in A_n, id=9648new! -- WP guess: conjugacy in A_n -- Status:
- PM: orbits of a normal subgroup are equal in size when the full group acts transitively, id=9646new! -- WP guess: orbits of a normal subgroup are equal in size when the full group acts transitively -- Status:
- PM: Kleene algebra, id=2618 -- WP: Kleene algebra -- Status: A
- PM: Kleene star, id=2584 -- WP: Kleene star -- Status: A
- PM: regular expression, id=2583 -- WP: regular expression -- Status:A
- PM: alternative treatment of concatenation, id=9774new! -- WP guess: alternative treatment of concatenation -- Status:
- PM: characterization of a Kleene algebra, id=9333new! -- WP guess: characterization of a Kleene algebra -- Status:
- PM: concatenation, id=9617new! -- WP guess: concatenation -- Status:
- PM: adjoining an identity to a semigroup, id=3410 -- WP guess: adjoining an identity to a semigroup -- Status:
- PM: bicyclic semigroup, id=3609 -- WP guess: bicyclic semigroup -- Status:
- PM: congruence, id=3403 -- WP guess: congruence -- Status:
- PM: cyclic semigroup, id=3559 -- WP guess: cyclic semigroup -- Status:
- PM: left identity and right identity, id=3435 -- WP guess: left identity and right identity -- Status:
- PM: null semigroup, id=3441 -- WP guess: null semigroup -- Status:
- PM: subsemigroup, submonoid, and subgroup, id=3434 -- WP guess: subsemigroup, submonoid, and subgroup -- Status:
- PM: zero elements, id=3440 -- WP: semigroup -- Status: NM
- PM: semigroup with two elements, id=8498new! -- WP guess: semigroup with two elements -- Status:
- PM: idempotency, id=2604 -- WP: idempotency -- Status: A
- PM: absorbing element, id=7727new! -- WP guess: absorbing element -- Status:
- PM: loop and quasigroup, id=3436 -- WP: quasigroup -- Status: A
- PM: Moufang loop, id=4578 -- WP guess: Moufang loop -- Status:
- PM: medial quasigroup, id=8617new! -- WP guess: medial quasigroup -- Status:
- PM: proof of example of medial quasigroup, id=8618new! -- WP guess: proof of example of medial quasigroup -- Status:
This page provides a list of all articles available at PlanetMath in the following topic:
- 20-XX Group theory and generalizations.
This list will be periodically updated. Each entry in the list has three fields:
- PM : The first field is the link to the PlanetMath article, along with the article's object ID.
- WP : The second field is either a "guessed" link to a correspondingly named Wikipedia article, produced by the script which generated the list, or one or more manually entered links to the corresponding Wikipedia articles on the subject.
- Status : The third field is the status field, which explains the current status of the entry. The recommended status entries are:
| Status | means PM article |
| N | not needed |
| A | adequately covered |
| C | copied |
| M | merged |
| NC | needs copying |
| NM | needs merging |
- Please update the WP and Status fields as appropriate.
- if the WP field is correct please remove the qualifier "guess".
- If the corresponding Wikipedia article exists, but the link to it is wrong, please fix the link.
- If you copy or merge an article from PlanetMath, please update the WP and Status fields for that entry.
- If you have any comments, for example, thoughts on how the PlanetMath article compares to the corresponding Wikipedia article(s), please place such comments on a new indented line following the entry. Comments of this kind are very valuable.
Don't forget to include the relevant template if you copy over text or feel like an external link is warranted
- {{planetmath|id=|title=}} for copied over text
- {{planetmath reference|id=|title=}} for an external link
See the main page for examples and usage criteria.
One can use the web-based program Pmform to convert PlanetMath articles to the Wikipedia format. As a side benefit, this tool will place the PlanetMath template for you.
- PM: alternating group is a normal subgroup of the symmetric group, id=4387 -- WP: symmetric group -- Status: A
- PM: associative, id=2150 -- WP: associative -- Status: A
- PM: bibliography for group theory, id=5683 -- WP: List of publications in mathematics#Group theory -- Status: NM
- PM: canonical projection, id=3950 -- WP: quotient group -- Status: A
- PM: centralizer, id=2833 -- WP: centralizer -- Status: A
- PM: commutative, id=2148 -- WP: commutative -- Status: A
- PM: examples of groups, id=3144 -- WP: examples of groups -- Status: NM
- PM: general associativity, id=6165 -- WP: general associativity -- Status: N
- PM: group, id=78 -- WP: group (mathematics) -- Status: A
- PM: groups of small order, id=6451 -- WP: examples of groups -- Status: NM
- PM: inverse forming in proportion to group operation, id=6575 -- WP guess: group (mathematics) -- Status: A
- PM: quotient group, id=1127 -- WP: quotient group -- Status: A
- PM: uniqueness of inverse (for groups), id=5687 -- WP guess: group (mathematics) -- Status: A
- PM: correspondence of normal subgroups and group congruences, id=7445 -- WP guess: correspondence of normal subgroups and group congruences -- Status:
- PM: cube of a number, id=6859 -- WP guess: cube of a number -- Status:
- PM: examples of non-commutative operations, id=6768 -- WP: Commutative operation -- Status: A
- PM: indecomposable group, id=7232 -- WP guess: indecomposable group -- Status:
- PM: proof that a subgroup of a group defines an equivalence relation on the group, id=7443 -- WP guess: proof that a subgroup of a group defines an equivalence relation on the group -- Status:
- PM: the alternating group has index 2 in the symmetric group, id=9048new! -- WP guess: the alternating group has index 2 in the symmetric group -- Status:
- PM: Bruhat decomposition, id=7669new! -- WP guess: Bruhat decomposition -- Status:
- PM: length function, id=4365 -- WP: length function -- Status: C
- PM: a characterization of groups, id=6391 -- WP: semigroup -- Status: NM
- PM: center, id=2191 -- WP: center of a group -- Status: A
- PM: characteristic subgroup, id=3180 -- WP: characteristic subgroup -- Status: A
- PM: class function, id=1847 -- WP: class function -- Status: A
- PM: conjugacy class, id=1848 -- WP: conjugacy class -- Status: A
- PM: conjugacy class formula, id=3624 -- WP: conjugacy class -- Status: A
- PM: conjugate stabilizer subgroups, id=3888 -- WP guess: conjugate stabilizer subgroups -- Status:
- PM: cyclic group, id=2185 -- WP: cyclic group -- Status: A
- PM: derived subgroup, id=2812 -- WP: derived subgroup -- Status: A
- PM: equivariant, id=4709 -- WP: equivariant -- Status: A
- PM: examples of finite simple groups, id=3568 -- WP: list of finite simple groups -- Status: A
- PM: Feit-Thompson theorem, id=4503 -- WP: Feit-Thompson theorem -- Status: A
- PM: finitely generated group, id=1726 -- WP: finitely generated group -- Status: A
- PM: fourth isomorphism theorem, id=4917 -- WP: isomorphism theorem -- Status: A
- PM: generator, id=4094 -- WP: generating set of a group -- Status: A
- PM: group actions and homomorphisms, id=3820 -- WP: group action -- Status: NM
- PM: group homomorphism, id=719 -- WP: group homomorphism -- Status: A
- PM: homogeneous space, id=4038 -- WP: group action -- Status: A
- PM: identity element, id=3140 -- WP: identity element -- Status: A
- PM: inner automorphism, id=3155 -- WP: inner automorphism -- Status: A
- PM: isomorphic groups, id=5127 -- WP: group (mathematics) -- Status: A
- PM: kernel, id=812 -- WP: group homomorphism -- Status: A
- PM: maximal, id=2198 -- WP: maximal subgroup -- Status: A
- PM: normal closure, id=6307 -- WP: normal closure -- Status: A
- PM: normal subgroup, id=1305 -- WP: normal subgroup -- Status: A
- PM: normality of subgroups is not transitive, id=3147 -- WP: normal subgroup -- Status: A
- PM: normalizer, id=2873 -- WP: normalizer -- Status: A
- PM: order (of a group), id=2871 -- WP guess: Group (mathematics) -- Status: A
- PM: presentation of a group, id=2182 -- WP guess: presentation of a group -- Status: A
- PM: proof of first isomorphism theorem, id=2922 -- WP guess: isomorphism theorem -- Status: N
- I've put an external link to PM proof AdamSmithee 09:09, 12 January 2006 (UTC)
- PM: proof of fourth isomorphism theorem, id=5749 -- WP guess: proof of fourth isomorphism theorem -- Status:
- PM: proof of second isomorphism theorem, id=3153 -- WP guess: isomorphism theorem -- Status: N
- I've put an external link to PM proof AdamSmithee 09:09, 12 January 2006 (UTC)
- PM: proof that all cyclic groups are abelian, id=4096 -- WP guess: proof that all cyclic groups are abelian -- Status:
- PM: proof that all cyclic groups of the same order are isomorphic to each other, id=4095 -- WP guess: proof that all cyclic groups of the same order are isomorphic to each other -- Status:
- PM: proof that all subgroups of a cyclic group are cyclic, id=4097 -- WP guess: proof that all subgroups of a cyclic group are cyclic -- Status:
- PM: Proof: The orbit of any element of a group is a subgroup, id=4102 -- WP guess: Proof: The orbit of any element of a group is a subgroup -- Status:
- PM: regular group action, id=3884 -- WP: regular group action -- Status: A
- PM: simple group, id=2189 -- WP: simple group -- Status: A
- PM: solvable group, id=1336 -- WP: solvable group -- Status: A
- PM: a subgroup of index 2 is normal, id=6905 -- WP guess: a subgroup of index 2 is normal -- Status:
- PM: core of a subgroup, id=7547 -- WP guess: core of a subgroup -- Status:
- PM: Fundamental homomorphism theorem, id=7495 -- WP guess: Fundamental homomorphism theorem -- Status:
- PM: generating set of a group, id=7545 -- WP guess: generating set of a group -- Status:
- PM: nonabelian group, id=5138 -- WP: nonabelian group -- Status:A
- PM: proof of third isomorphism theorem, id=7496 -- WP: isomorphism theorem -- Status: N
- I added an external link to the proof AdamSmithee 08:51, 7 March 2006 (UTC)
- PM: a group of even order contains an element of order 2, id=9512new! -- WP guess: a group of even order contains an element of order 2 -- Status:
- PM: double coset, id=8408new! -- WP guess: double coset -- Status:
- PM: groups with abelian inner automorphism group, id=9799new! -- WP guess: groups with abelian inner automorphism group -- Status:
- PM: homogeneous group, id=8298new! -- WP guess: homogeneous group -- Status:
- PM: normality of subgroups of prime index, id=9825new! -- WP guess: normality of subgroups of prime index -- Status:
- PM: one-sided normality of subsemigroup, id=8265new! -- WP guess: one-sided normality of subsemigroup -- Status:
- PM: order of elements in finite groups, id=8757new! -- WP guess: order of elements in finite groups -- Status:
- PM: the derived subgroup is normal, id=8135new! -- WP guess: the derived subgroup is normal -- Status:
- PM: the kernel of a group homomorphism is a normal subgroup, id=9698new! -- WP guess: the kernel of a group homomorphism is a normal subgroup -- Status:
- PM: Cayley table, id=3540 -- WP: Cayley table -- Status: A
- PM: direct product and restricted direct product of groups, id=6560 -- WP: direct product, direct sum-- Status: NM
- Some work needs to be done here to draw the distinctions between direct sum and direct product. Merging together the two articles might be a good idea. Jtwdog 17:50, 26 October 2005 (UTC)
- PM: proper subgroup, id=3141 -- WP: proper subgroup -- Status: A
- PM: quaternion group, id=2844 -- WP: quaternion group -- Status: A
- PM: generalized quaternion group, id=8620new! -- WP guess: generalized quaternion group -- Status:
- PM: proof that G is cyclic if and only if \lvert G \rvert=\exp(G), id=8759new! -- WP guess: proof that G is cyclic if and only if \lvert G \rvert=\exp(G) -- Status:
- PM: proof that a finite abelian group has element with \lvert g\rvert=\exp(G), id=8758new! -- WP guess: proof that a finite abelian group has element with \lvert g\rvert=\exp(G) -- Status:
- PM: permutation group, id=3758 -- WP: permutation group -- Status: A
- PM: blocks of permutation groups, id=9668new! -- WP guess: blocks of permutation groups -- Status:
- PM: conjugacy classes in the symmetric group S_n, id=9613new! -- WP guess: conjugacy classes in the symmetric group S_n -- Status:
- PM: primitive permutation group, id=4913 -- WP: primitive permutation group -- Status: A
- PM: doubly transitive groups are primitive, id=9724new! -- WP guess: doubly transitive groups are primitive -- Status:
- PM: examples of primitive groups that are not doubly transitive, id=9742new! -- WP guess: examples of primitive groups that are not doubly transitive -- Status:
- PM: transitive actions are primitive if and only if stabilizers are maximal subgroups, id=9669new! -- WP guess: transitive actions are primitive if and only if stabilizers are maximal subgroups -- Status:
- PM: Jordan's theorem (multiply transitive groups), id=3761 -- WP: Mathieu group -- Status: M
- PM: multiply transitive, id=3759 -- WP: multiply transitive -- Status: M
- PM: sharply multiply transitive, id=3760 -- WP: sharply multiply transitive -- Status: M
- PM: alternative characterization of multiply transitive permutation groups, id=9723new! -- WP guess: alternative characterization of multiply transitive permutation groups -- Status:
- PM: example of multiply transitive, id=9726new! -- WP guess: example of multiply transitive -- Status:
- PM: symmetric group, id=5421 -- WP: symmetric group -- Status: A
- PM: symmetric group, id=1040 -- WP: symmetric group -- Status:A
- PM: symmetric group is generated by adjacent transpositions, id=9054new! -- WP guess: symmetric group is generated by adjacent transpositions -- Status:
- PM: symmetric group on three letters, id=7870new! -- WP guess: symmetric group on three letters -- Status:
- PM: two isomorphic groups, id=7871new! -- WP guess: two isomorphic groups -- Status:
- PM: Cayley's theorem, id=2174 -- WP: permutation group -- Status: A
- PM: finding the order of a group, id=7904new! -- WP guess: finding the order of a group -- Status:
- PM: Frobenius group, id=3757 -- WP: Frobenius group -- Status: A
- PM: proof of Cayley's theorem, id=2751 -- WP guess: proof of Cayley's theorem -- Status:N
- PM: permutation group on a set, id=5022 -- WP guess: permutation group on a set -- Status:
- PM: a representation which is not completely reducible, id=4122 -- WP: Maschke's theorem -- Status: NM
- It's nice to include counter-examples, though this is probably a low priority. Jtwdog 20:26, 26 October 2005 (UTC)
- PM: Maschke's theorem, id=3874 -- WP: Maschke's theorem -- Status: A
- PM: orthogonality relations, id=3878 -- WP: orthogonality relations -- Status: A
- It would be nice to bring over a little of the proof, as I think it's quite beautiful, but I'll leave that to other's judgement. Jtwdog 20:26, 26 October 2005 (UTC)
- PM: Schur's lemma, id=3570 -- WP: Schur's lemma -- Status: A
- PM: example of immanent, id=5479 -- WP guess: example of immanent -- Status:
- PM: unitary representation, id=9111new! -- WP guess: unitary representation -- Status:
- PM: G-module, id=6663 -- WP: group algebra -- Status: A
- PM: character, id=1843 -- WP: character theory -- Status: A
- PM: example of induced representation, id=6160 -- WP guess: example of induced representation -- Status: N
- PM: example of matrix representations, id=6573 -- WP guess: example of matrix representations -- Status: N
- PM: Frobenius reciprocity, id=1842 -- WP: Frobenius reciprocity -- Status: A
- PM: group representation, id=1596 -- WP: group representation -- Status: A
- PM: induced representation, id=1823 -- WP: induced representation -- Status: A
- PM: matrix representation, id=6581 -- WP: group representation -- Status: A
- PM: regular representation, id=1828 -- WP: regular representation -- Status: A
- PM: restriction representation, id=1822 -- WP: restricted representation -- Status: A
- PM: irreducible representations of S_n, id=9566new! -- WP guess: irreducible representations of S_n -- Status:
- PM: proof that dimension of complex irreducible representation divides order of group, id=9460new! -- WP guess: proof that dimension of complex irreducible representation divides order of group -- Status:
- PM: quotient representations, id=8834new! -- WP guess: quotient representations -- Status:
- PM: Burnside p-q theorem, id=3747 -- WP guess: Burnside p-q theorem -- Status:
- PM: classification of semisimple groups, id=3772 -- WP guess: classification of semisimple groups -- Status:
- PM: semisimple group, id=3771 -- WP guess: semisimple group -- Status: A
- PM: Burnside's Theorem, id=8839new! -- WP guess: Burnside's Theorem -- Status:
- PM: simplicity of the alternating groups, id=3569 -- WP guess: simplicity of the alternating groups -- Status:N
- Jtwdog 04:09, 28 October 2005 (UTC)
- Its a proof; added ref to simple group. linas 23:03, 6 April 2007 (UTC)
- PM: example of infinite simple group, id=9148new! -- WP guess: example of infinite simple group -- Status:
- PM: Janko groups, id=4762 -- WP: list of finite simple groups -- Status: A
- PM: supersolvable group, id=4751 -- WP guess: supersolvable group -- Status:
- PM: Čuhinin's theorem, id=3798 -- WP guess: Čuhinin's theorem -- Status:
- PM: Wielandt-Kegel theorem, id=8412new! -- WP guess: Wielandt-Kegel theorem -- Status:
- PM: Burnside basis theorem, id=3750 -- WP guess: Burnside basis theorem -- Status:
- PM: classification of finite nilpotent groups, id=3755 -- WP guess: classification of finite nilpotent groups -- Status:
- PM: finite nilpotent groups, id=7735new! -- WP guess: finite nilpotent groups -- Status:
- PM: Frattini subset, id=8693new! -- WP guess: Frattini subset -- Status:
- PM: proof of the Burnside basis theorem, id=7731new! -- WP guess: proof of the Burnside basis theorem -- Status:
- PM: p-subgroup, id=5184 -- WP guess: p-subgroup -- Status:
- PM: \pi-groups and \pi'-groups, id=3797 -- WP guess: \pi-groups and \pi'-groups -- Status:
- PM: a nontrivial normal subgroup of a finite p-group G and the center of G have nontrivial intersection, id=5827 -- WP guess: a nontrivial normal subgroup of a finite p-group G and the center of G have nontrivial intersection -- Status:
- PM: Burnside normal complement theorem, id=3754 -- WP guess: Burnside normal complement theorem -- Status:
- PM: class equation theorem, id=5821 -- WP guess: class equation theorem -- Status:
- PM: example of groups of order pq, id=6526 -- WP guess: example of groups of order pq -- Status:
- PM: Frattini argument, id=3748 -- WP guess: Frattini argument -- Status:
- PM: groups of order pq, id=3183 -- WP guess: groups of order pq -- Status:
- PM: p-primary component, id=4610 -- WP guess: p-primary component -- Status:
- PM: proof of class equation theorem, id=5823 -- WP guess: proof of class equation theorem -- Status:
- PM: proof of Frattini argument, id=3749 -- WP guess: proof of Frattini argument -- Status:
- PM: proof of Sylow theorems, id=3182 -- WP guess: proof of Sylow theorems -- Status:
- PM: proof that a nontrivial normal subgroup of a finite p-group G and the center of G have nontrivial intersection, id=5828 -- WP guess: proof that a nontrivial normal subgroup of a finite p-group G and the center of G have nontrivial intersection -- Status:
- PM: subgroups containing the normalizers of Sylow subgroups normalize themselves, id=3763 -- WP guess: subgroups containing the normalizers of Sylow subgroups normalize themselves -- Status:
- PM: Sylow p-subgroups, id=5135 -- WP guess: Sylow p-subgroups -- Status:
- PM: Sylow p-subgroup, id=3181 -- WP guess: Sylow p-subgroup -- Status:
- PM: Sylow theorems, id=2243 -- WP guess: Sylow theorems -- Status:
- PM: Sylow's first theorem, id=4910 -- WP guess: Sylow's first theorem -- Status:
- PM: Sylow's third theorem, id=4899 -- WP guess: Sylow's third theorem -- Status:
- PM: characteristically simple group, id=3767 -- WP guess: characteristically simple group -- Status:
- PM: Fitting's theorem, id=4600 -- WP guess: Fitting's theorem -- Status:
- PM: the Frattini subgroup of a finite group is nilpotent, id=3762 -- WP guess: the Frattini subgroup of a finite group is nilpotent -- Status:
- PM: maximal condition, id=4752 -- WP guess: maximal condition -- Status:
- PM: minimal condition, id=4753 -- WP guess: minimal condition -- Status:
- PM: subnormal series, id=4750 -- WP guess: subnormal series -- Status:
- PM: subnormal subgroup, id=3756 -- WP: subnormal subgroup -- Status: A
- PM: Order Conjecture for non-commuting graph of a group, id=7119 -- WP guess: Order Conjecture for non-commuting graph of a group -- Status:
- PM: Cauchy's theorem, id=1569 -- WP: Cauchy's theorem (group theory) -- Status: C
- The ling is currently redirecting to Order (group theory), which mentions the theorem in passing (anyway, the article should be cleaned up). I think that something more like Lagrange's theorem (group theory) would be more appropriate AdamSmithee 09:28, 12 January 2006 (UTC)
- Done AdamSmithee 09:26, 7 March 2006 (UTC)
- PM: exponent, id=4087 -- WP: exponent (group theory) -- Status: A
- PM: fully invariant subgroup, id=3684 -- WP guess: fully invariant subgroup -- Status:
- PM: Lagrange's theorem, id=1566 -- WP: Lagrange's theorem (group theory) -- Status: A
- PM: proof of Cauchy's theorem, id=2186 -- WP: Cauchy's theorem (group theory) -- Status: N
- NM after creation of the WP article - see above AdamSmithee 09:28, 12 January 2006 (UTC)
- Actually, on a second thought, this is not a particularly illuminating proof. I linked to it AdamSmithee 09:26, 7 March 2006 (UTC)
- PM: proof of Cauchy's theorem in abelian case, id=6045 -- WP guess: proof of Cauchy's theorem in abelian case -- Status:
- PM: proof of Lagrange's theorem, id=1663 -- WP: Lagrange's theorem (group theory) -- Status: A
- PM: proof of the converse of Lagrange's theorem for finite cyclic groups, id=4089 -- WP guess: proof of the converse of Lagrange's theorem for finite cyclic groups -- Status:
- PM: proof that \operatorname{exp}~G divides |G|, id=4091 -- WP guess: G| -- Status:
- PM: proof that |g| divides \operatorname{exp}~G, id=4092 -- WP guess: g| divides \operatornameexp~G -- Status:
- PM: proof that every group of prime order is cyclic, id=4101 -- WP guess: proof that every group of prime order is cyclic -- Status:
- PM: calculus of subgroup orders, id=7766new! -- WP guess: calculus of subgroup orders -- Status:
- PM: example of a non-fully invariant subgroup, id=8172new! -- WP guess: example of a non-fully invariant subgroup -- Status:
- PM: example of fully invariant subgroup, id=8136new! -- WP guess: example of fully invariant subgroup -- Status:
- PM: free group, id=2687 -- WP guess: free group -- Status:
- PM: Nielsen-Schreier theorem, id=3251 -- WP guess: Nielsen-Schreier theorem -- Status:
- PM: proof of Nielsen-Schreier theorem and Schreier index formula, id=4693 -- WP guess: proof of Nielsen-Schreier theorem and Schreier index formula -- Status:
- PM: Schreier index formula, id=4699 -- WP guess: Schreier index formula -- Status:
- PM: reduced word, id=8289new! -- WP guess: reduced word -- Status:
20E06 Free products, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations
- PM: free product, id=6574 -- WP: free product -- Status: NM
- PM: free product with amalgamated subgroup, id=3944 -- WP: free product with amalgamated subgroup -- Status: NM
- PM: HNN extension, id=8122new! -- WP guess: HNN extension -- Status:
- PM: A finitely generated group has only finitely many subgroups of a given index, id=7054 -- WP guess: A finitely generated group has only finitely many subgroups of a given index -- Status:
- PM: Zeta function of a group, id=7053 -- WP guess: Zeta function of a group -- Status:
- PM: example of non-permutable subgroup, id=8375new! -- WP guess: example of non-permutable subgroup -- Status:
- PM: permutable subgroup, id=8372new! -- WP guess: permutable subgroup -- Status:
- PM: metabelian group, id=7532 -- WP guess: metabelian group -- Status:
- PM: example of a Jordan-Hölder decomposition, id=5911 -- WP guess: example of a Jordan-Hölder decomposition -- Status:
- PM: Jordan-Hölder decomposition, id=1332 -- WP guess: Jordan-Hölder decomposition -- Status:
- PM: Schreier refinement theorem, id=6286 -- WP guess: Schreier refinement theorem -- Status:
- PM: ascending series, id=8353new! -- WP guess: ascending series -- Status:
- PM: descending series, id=8352new! -- WP guess: descending series -- Status:
- PM: lattice of subgroups, id=7756new! -- WP guess: lattice of subgroups -- Status:
- PM: normal subgroups form sublattice of a subgroup lattice, id=7770new! -- WP guess: normal subgroups form sublattice of a subgroup lattice -- Status:
- PM: profinite group, id=3134 -- WP: profinite group -- Status: A
- PM: A groups embeds into its profinite completion if and only if it is residually finite, id=7052 -- WP guess: A groups embeds into its profinite completion if and only if it is residually finite -- Status:
- PM: order of a profinite group, id=7228 -- WP guess: order of a profinite group -- Status:
- PM: pro-p group, id=6900 -- WP guess: pro-p group -- Status:
- PM: procyclic group, id=6901 -- WP guess: procyclic group -- Status:
- PM: Profinite completion, id=7051 -- WP guess: Profinite completion -- Status:
- PM: supernatural number, id=7227 -- WP guess: supernatural number -- Status:
- PM: generalized dihedral group, id=6572 -- WP guess: generalized dihedral group -- Status:
- PM: proof of the Jordan Holder decomposition theorem, id=1335 -- WP guess: proof of the Jordan Holder decomposition theorem -- Status:
- PM: semidirect product of groups, id=2829 -- WP guess: semidirect product of groups -- Status:
- PM: wreath product, id=3505 -- WP guess: wreath product -- Status:
- PM: semi-direct factor and quotient group, id=6924 -- WP guess: semi-direct factor and quotient group -- Status:
- PM: examples of semidirect products of groups, id=9747new! -- WP guess: examples of semidirect products of groups -- Status:
- PM: holomorph of a group, id=9746new! -- WP guess: holomorph of a group -- Status:
- PM: virtually cyclic group, id=7746new! -- WP guess: virtually cyclic group -- Status:
- PM: locally \cal P, id=5782 -- WP guess: locally \cal P -- Status:
- PM: locally cyclic group, id=4497 -- WP: locally cyclic group -- Status: A
- PM: subgoups of locally cyclic groups are locally cyclic, id=9577new! -- WP guess: subgoups of locally cyclic groups are locally cyclic -- Status:
- PM: residually \cal P, id=6570 -- WP guess: residually \cal P -- Status:
- PM: subdirect product of groups, id=6571 -- WP guess: subdirect product of groups -- Status:
- PM: existence of maximal subgroups, id=8564new! -- WP guess: existence of maximal subgroups -- Status:
- PM: Jordan-Hölder decomposition theorem, id=1333 -- WP guess: Jordan-Hölder decomposition theorem -- Status:
- PM: homomorphisms of simple groups, id=7644new! -- WP guess: homomorphisms of simple groups -- Status:
- PM: property of infinite simple group, id=8213new! -- WP guess: property of infinite simple group -- Status:
- PM: abelian groups of order 120, id=4654 -- WP guess: abelian groups of order 120 -- Status:
- PM: fundamental theorem of finitely generated abelian groups, id=4652 -- WP guess: fundamental theorem of finitely generated abelian groups -- Status:
- PM: group socle, id=7925new! -- WP guess: group socle -- Status:
- PM: complete group, id=7186 -- WP guess: complete group -- Status:
- PM: conjugacy class, id=5042 -- WP: conjugacy class -- Status: A
- PM: Frattini subgroup, id=2192 -- WP: Frattini subgroup -- Status: A
- PM: non-generator, id=2196 -- WP: non-generator -- Status: A
- PM: abnormal subgroup, id=8635new! -- WP guess: abnormal subgroup -- Status:
- PM: pronormal subgroup, id=8634new! -- WP guess: pronormal subgroup -- Status:
- PM: virtually abelian group, id=6168new! -- WP guess: virtually abelian group -- Status:
- PM: triangle groups, id=5925 -- WP guess: triangle groups -- Status:
- PM: Baumslag-Solitar group, id=9794new! -- WP guess: Baumslag-Solitar group -- Status:
- PM: hyperbolic metric space, id=9509new! -- WP guess: hyperbolic metric space -- Status:
- PM: automatic group, id=5735 -- WP guess: automatic group -- Status:
- PM: Tietze transform, id=7658new! -- WP guess: Tietze transform -- Status:
- PM: properties of group commutators and commutator subgroups, id=7381 -- WP guess: properties of group commutators and commutator subgroups -- Status:
- PM: abelianization, id=6561 -- WP guess: abelianization -- Status:
- PM: transfinite derived series, id=5727 -- WP guess: transfinite derived series -- Status:
- PM: polycyclic group, id=6285 -- WP guess: polycyclic group -- Status:
- PM: metacyclic group, id=7531 -- WP guess: metacyclic group -- Status:
- PM: nilpotent group, id=3113 -- WP: nilpotent group -- Status: A
- PM: Hamiltonian group, id=7520 -- WP guess: Hamiltonian group -- Status:
- PM: enumerating groups, id=7849new! -- WP guess: enumerating groups -- Status:
- PM: locally nilpotent group, id=7619 -- WP guess: locally nilpotent group -- Status:
- PM: normalizer condition, id=8348new! -- WP guess: normalizer condition -- Status:
- PM: inverse limit, id=4655 -- WP: inverse limit -- Status: NM
- PM: outer automorphism group, id=4993 -- WP guess: outer automorphism group -- Status:
- PM: examples of outer automorphism group, id=8682new! -- WP guess: examples of outer automorphism group -- Status:
- PM: braid group, id=4604 -- WP: braid group -- Status: A
- PM: elementary abelian group, id=6566 -- WP guess: elementary abelian group -- Status:
- PM: locally finite group, id=5776 -- WP guess: locally finite group -- Status:
- PM: proof that local finiteness is closed under extension, id=7538 -- WP guess: proof that local finiteness is closed under extension -- Status:
- PM: periodic group, id=7511 -- WP guess: periodic group -- Status:
- PM: quasicyclic group, id=7500 -- WP guess: quasicyclic group -- Status:
- PM: Chernikov group, id=7769new! -- WP guess: Chernikov group -- Status:
- PM: Tarski group, id=7722new! -- WP guess: Tarski group -- Status:
- PM: dihedral group, id=2159 -- WP: dihedral group -- Status: A
- PM: octic group, id=6453 -- WP: dihedral group -- Status: A
- PM: Coxeter group, id=7570 -- WP guess: Coxeter group -- Status:
- PM: dihedral group properties, id=8175new! -- WP guess: dihedral group properties -- Status:
- PM: groups that act freely on trees are free, id=4656 -- WP guess: groups that act freely on trees are free -- Status:
- PM: graph product of groups, id=8263new! -- WP guess: graph product of groups -- Status:
- PM: ping-pong lemma, id=9507new! -- WP guess: ping-pong lemma -- Status:
- PM: perfect group, id=4701 -- WP: perfect group -- Status: A
- PM: essential subgroup, id=7387 -- WP guess: essential subgroup -- Status:
- PM: Hopfian group, id=7516 -- WP guess: Hopfian group -- Status:
- PM: section of a group, id=9584new! -- WP guess: section of a group -- Status:
- PM: computation of the order of GL(n, F_q), id=3541 -- WP guess: computation of the order of GL(n, F_q) -- Status:
- PM: general linear group, id=2462 -- WP guess: general linear group -- Status:
- PM: Nagao's theorem, id=4747 -- WP guess: Nagao's theorem -- Status:
- PM: special linear group, id=2463 -- WP guess: special linear group -- Status:
- PM: theorems of general linear group over a finite field, id=3529 -- WP guess: theorems of general linear group over a finite field -- Status:
- PM: theorems of special linear group over a finite field, id=6620 -- WP guess: theorems of special linear group over a finite field -- Status:
- PM: \mathit{SL}(2,\mathbb{F}_p) has no 1 dimensional irreducible representations over \mathbb{F}_p, id=6915 -- WP guess: \mathitSL(2,\mathbbF_p) has no 1 dimensional irreducible representations over \mathbbF_p -- Status:
- PM: irreducible representations of the special linear group over \mathbb{F}_p, id=6914 -- WP guess: irreducible representations of the special linear group over \mathbbF_p -- Status:
- PM: projective special linear group, id=6912 -- WP guess: projective special linear group -- Status:
- PM: GL_2(\mathbb{Z}), id=8707new! -- WP guess: GL_2(\mathbbZ) -- Status:
- PM: orthogonal group, id=2482 -- WP: orthogonal group -- Status: A
- PM: Ihara's theorem, id=4657 -- WP guess: Ihara's theorem -- Status:
- PM: \mathit{SL}_2(F_3), id=4873 -- WP guess: \mathitSL_2(F_3) -- Status:
- PM: group extension, id=7246 -- WP guess: group extension -- Status:
- PM: factor system, id=5887 -- WP guess: group cohomology -- Status: A
- PM: group cohomology, id=4571 -- WP guess: group cohomology -- Status: A
- PM: stronger Hilbert theorem 90, id=4577 -- WP guess: Hilbert's theorem 90 -- Status: NM
- PM: variety of groups, id=3662 -- WP guess: variety of groups -- Status:
- PM: Schinzel's theorem, id=1115 -- WP guess: Schinzel's theorem -- Status:
- PM: Baer-Specker group, id=7344 -- WP guess: Baer-Specker group -- Status:
- PM: direct product of groups, id=2180 -- WP guess: direct product of groups -- Status:
- PM: example of Schreier's Lemma, id=7903new! -- WP guess: example of Schreier's Lemma -- Status:
- PM: Schreier's lemma, id=7901new! -- WP guess: Schreier's lemma -- Status:
- PM: transversals / lifts / sifts, id=7900new! -- WP guess: transversals / lifts / sifts -- Status:
- PM: divisible closure, id=7993new! -- WP guess: divisible closure -- Status:
- PM: divisible group, id=4499 -- WP: divisible group -- Status: A
- PM: example of divisible group, id=4500 -- WP: divisible group -- Status: N
- PM: Klein 4-group, id=3139 -- WP: Klein 4-group -- Status: A
- PM: abelian group, id=5107 -- WP guess: abelian group -- Status:
- PM: n-divisible group, id=9841new! -- WP guess: n-divisible group -- Status:
- PM: example of Munn tree, id=8294new! -- WP guess: example of Munn tree -- Status:
- PM: free semigroup, id=8287new! -- WP guess: free semigroup -- Status:
- PM: prefix set, id=8292new! -- WP guess: prefix set -- Status:
- PM: presentation of inverse monoids and inverse semigroups, id=8271new! -- WP guess: presentation of inverse monoids and inverse semigroups -- Status:
- PM: Schützenberger graph, id=8268new! -- WP guess: Schützenberger graph -- Status:
- PM: Wagner congruence, id=8272new! -- WP guess: Wagner congruence -- Status:
- PM: word problem, id=8301new! -- WP guess: word problem -- Status:
- PM: existence of maximal semilattice decomposition, id=3553 -- WP guess: existence of maximal semilattice decomposition -- Status:
- PM: Rees factor, id=3517 -- WP guess: Rees factor -- Status:
- PM: semilattice decomposition of a semigroup, id=3552 -- WP guess: semilattice decomposition of a semigroup -- Status:
- PM: simple semigroup, id=3521 -- WP guess: simple semigroup -- Status:
- PM: cancellative semigroup, id=5926 -- WP guess: cancellative semigroup -- Status:
- PM: completely simple semigroup, id=6153new! -- WP guess: completely simple semigroup -- Status:
- PM: free semigroup with involution, id=8283new! -- WP guess: free semigroup with involution -- Status:
- PM: I-semigroup, id=8282new! -- WP guess: I-semigroup -- Status:
- PM: semigroup with involution, id=8281new! -- WP guess: semigroup with involution -- Status:
- PM: Archimedean semigroup, id=3572 -- WP guess: Archimedean semigroup -- Status:
- PM: commutative semigroup, id=3573 -- WP guess: commutative semigroup -- Status:
- PM: regular semigroup, id=5883 -- WP guess: regular semigroup -- Status:
- PM: McAlister covering theorem, id=6201 -- WP guess: McAlister covering theorem -- Status:
- PM: symmetric inverse semigroup, id=8274new! -- WP guess: symmetric inverse semigroup -- Status:
- PM: Wagner-Preston representation theorem, id=8275new! -- WP guess: Wagner-Preston representation theorem -- Status:
- PM: semigroup of transformations, id=3561 -- WP guess: semigroup of transformations -- Status:
- PM: counting theorem, id=2127 -- WP: group action -- Status: A
- PM: example of counting theorem, id=5957 -- WP: group action -- Status: N
- PM: orbit, id=1517 -- WP: group action -- Status: A
- PM: orbit-stabilizer theorem, id=2173 -- WP: group action -- Status: A
- PM: proof of counting theorem, id=3099 -- WP: group action -- Status: N
- PM: proof of orbit-stabilizer theorem, id=2315 -- WP: group action -- Status: N
- PM: simply transitive, id=6208 -- WP: simply transitive -- Status: A
- PM: centralizer of a k-cycle, id=9647new! -- WP guess: centralizer of a k-cycle -- Status:
- PM: conjugacy in A_n, id=9648new! -- WP guess: conjugacy in A_n -- Status:
- PM: orbits of a normal subgroup are equal in size when the full group acts transitively, id=9646new! -- WP guess: orbits of a normal subgroup are equal in size when the full group acts transitively -- Status:
- PM: Kleene algebra, id=2618 -- WP: Kleene algebra -- Status: A
- PM: Kleene star, id=2584 -- WP: Kleene star -- Status: A
- PM: regular expression, id=2583 -- WP: regular expression -- Status:A
- PM: alternative treatment of concatenation, id=9774new! -- WP guess: alternative treatment of concatenation -- Status:
- PM: characterization of a Kleene algebra, id=9333new! -- WP guess: characterization of a Kleene algebra -- Status:
- PM: concatenation, id=9617new! -- WP guess: concatenation -- Status:
- PM: adjoining an identity to a semigroup, id=3410 -- WP guess: adjoining an identity to a semigroup -- Status:
- PM: bicyclic semigroup, id=3609 -- WP guess: bicyclic semigroup -- Status:
- PM: congruence, id=3403 -- WP guess: congruence -- Status:
- PM: cyclic semigroup, id=3559 -- WP guess: cyclic semigroup -- Status:
- PM: left identity and right identity, id=3435 -- WP guess: left identity and right identity -- Status:
- PM: null semigroup, id=3441 -- WP guess: null semigroup -- Status:
- PM: subsemigroup, submonoid, and subgroup, id=3434 -- WP guess: subsemigroup, submonoid, and subgroup -- Status:
- PM: zero elements, id=3440 -- WP: semigroup -- Status: NM
- PM: semigroup with two elements, id=8498new! -- WP guess: semigroup with two elements -- Status:
- PM: idempotency, id=2604 -- WP: idempotency -- Status: A
- PM: absorbing element, id=7727new! -- WP guess: absorbing element -- Status:
- PM: loop and quasigroup, id=3436 -- WP: quasigroup -- Status: A
- PM: Moufang loop, id=4578 -- WP guess: Moufang loop -- Status:
- PM: medial quasigroup, id=8617new! -- WP guess: medial quasigroup -- Status:
- PM: proof of example of medial quasigroup, id=8618new! -- WP guess: proof of example of medial quasigroup -- Status: