This article was nominated for deletion on 23 September 2012. The result of the discussion was keep. |
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As requested by Arthur Rubin, my justifications for adding this new proof to teh article are:
Also, it could be improved and made shorter, without extra complexity.
-- AYGHOR ( talk) 09:36, 25 May 2012 (UTC)
There was a body of opinion at Wikipedia:Articles for deletion/Fundamental theorem of cyclic groups that this article should be merged into Cyclic group: I don't think it can quite be described as the consensus, though. My point was that while this is clearly a name for the theorem, there seems no reason to believe that it is the name. There is essentially only one book in Google Books using this name (the alternative name "Characterization Theorem for Cyclic Groups" mentioned above scores two) and 12 hits for the phrase on Google Scholar. Compare with 37,700 hits on Google Books for "Fundamental theorem of algebra". Deltahedron ( talk) 18:07, 30 September 2012 (UTC)
Of the three references for the theorem only [1] uses the name "Fundamental Theorem". Only reference [2] includes the part "For the infinite cyclic group, every subgroup is infinite cyclic, of finite index, and for each integer i there is exactly one subgroup of index i". I know that it's both true and simple to prove. It may even be included in other nearby propositions or theorems. But it doesn't seem right to include it from a reference that doesn't include the name of the theorem. I've removed the sentence. Dingo1729 ( talk) 03:44, 2 October 2012 (UTC)
The result of the move request was: Moved. Beyond the change in the title, it looks like anyone who wants to perform the merge into Cyclic groups has the support of other editors to do so. EdJohnston ( talk) 21:42, 11 December 2013 (UTC) EdJohnston ( talk) 21:42, 11 December 2013 (UTC)
Fundamental theorem of cyclic groups → Subgroups of cyclic groups – We have lots of high-quality textbook sources covering the topic of subgroups of cyclic groups (the content of this article regardless of what it's called), so I think it is a worthy subject for an article (subsidiary to the main cyclic group article per Wikipedia:Summary style). However, I agree with the criticism above that the name "fundamental theorem of..." is not the best choice. The proposed move might ease some of the objections to this article, which as I understand it are that this is not fundamental enough to be called a fundamental theorem and that really only one source uses that name. Although most Wikipedia article titles are singular I think plural works better in this case because most of the material in the article considers all subgroups at once rather than a single subgroup in isolation. --Relisted. — Amakuru ( talk) 13:26, 2 December 2013 (UTC) David Eppstein ( talk) 03:41, 24 November 2013 (UTC) Support. Though I still think this should be shortened and merged into Cyclic groups. At some stage the amount of stuff we write obscures the basic simplicity of these groups. (That wasn't meant to mean they are all simple groups.) Dingo1729 ( talk) 16:45, 24 November 2013 (UTC)
Support/merge: actually I still think the merger is a good idea. The problem remains: why do we need a "separate article" on subgroups of a cyclic group, a theorem about it or otherwise. If cyclic group gets too long, we can always split it off. It should also be pointed out that cyclic group already has a discussion on subgroups. -- Taku ( talk) 16:32, 25 November 2013 (UTC)
Support/merge: although I admire Joe Gallian as an expositor and cheerleader, he can push the envelope a little too far at times. This is a case in point. In the article referenced, he makes his case for calling this result the Fundamental Theorem of Cyclic Groups, but the argument does not convince and the term did not catch on (it is hard to call what Herstein has as an easy exercise, a fundamental theorem). The result belongs in the cyclic group article–that is where readers should expect it to be, so I support a merge, but failing that, the title really needs to be changed as this is not what the result is commonly known as. Bill Cherowitzo ( talk) 04:56, 10 December 2013 (UTC)
This article was nominated for deletion on 23 September 2012. The result of the discussion was keep. |
This article is rated Start-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | |||||||||||
|
As requested by Arthur Rubin, my justifications for adding this new proof to teh article are:
Also, it could be improved and made shorter, without extra complexity.
-- AYGHOR ( talk) 09:36, 25 May 2012 (UTC)
There was a body of opinion at Wikipedia:Articles for deletion/Fundamental theorem of cyclic groups that this article should be merged into Cyclic group: I don't think it can quite be described as the consensus, though. My point was that while this is clearly a name for the theorem, there seems no reason to believe that it is the name. There is essentially only one book in Google Books using this name (the alternative name "Characterization Theorem for Cyclic Groups" mentioned above scores two) and 12 hits for the phrase on Google Scholar. Compare with 37,700 hits on Google Books for "Fundamental theorem of algebra". Deltahedron ( talk) 18:07, 30 September 2012 (UTC)
Of the three references for the theorem only [1] uses the name "Fundamental Theorem". Only reference [2] includes the part "For the infinite cyclic group, every subgroup is infinite cyclic, of finite index, and for each integer i there is exactly one subgroup of index i". I know that it's both true and simple to prove. It may even be included in other nearby propositions or theorems. But it doesn't seem right to include it from a reference that doesn't include the name of the theorem. I've removed the sentence. Dingo1729 ( talk) 03:44, 2 October 2012 (UTC)
The result of the move request was: Moved. Beyond the change in the title, it looks like anyone who wants to perform the merge into Cyclic groups has the support of other editors to do so. EdJohnston ( talk) 21:42, 11 December 2013 (UTC) EdJohnston ( talk) 21:42, 11 December 2013 (UTC)
Fundamental theorem of cyclic groups → Subgroups of cyclic groups – We have lots of high-quality textbook sources covering the topic of subgroups of cyclic groups (the content of this article regardless of what it's called), so I think it is a worthy subject for an article (subsidiary to the main cyclic group article per Wikipedia:Summary style). However, I agree with the criticism above that the name "fundamental theorem of..." is not the best choice. The proposed move might ease some of the objections to this article, which as I understand it are that this is not fundamental enough to be called a fundamental theorem and that really only one source uses that name. Although most Wikipedia article titles are singular I think plural works better in this case because most of the material in the article considers all subgroups at once rather than a single subgroup in isolation. --Relisted. — Amakuru ( talk) 13:26, 2 December 2013 (UTC) David Eppstein ( talk) 03:41, 24 November 2013 (UTC) Support. Though I still think this should be shortened and merged into Cyclic groups. At some stage the amount of stuff we write obscures the basic simplicity of these groups. (That wasn't meant to mean they are all simple groups.) Dingo1729 ( talk) 16:45, 24 November 2013 (UTC)
Support/merge: actually I still think the merger is a good idea. The problem remains: why do we need a "separate article" on subgroups of a cyclic group, a theorem about it or otherwise. If cyclic group gets too long, we can always split it off. It should also be pointed out that cyclic group already has a discussion on subgroups. -- Taku ( talk) 16:32, 25 November 2013 (UTC)
Support/merge: although I admire Joe Gallian as an expositor and cheerleader, he can push the envelope a little too far at times. This is a case in point. In the article referenced, he makes his case for calling this result the Fundamental Theorem of Cyclic Groups, but the argument does not convince and the term did not catch on (it is hard to call what Herstein has as an easy exercise, a fundamental theorem). The result belongs in the cyclic group article–that is where readers should expect it to be, so I support a merge, but failing that, the title really needs to be changed as this is not what the result is commonly known as. Bill Cherowitzo ( talk) 04:56, 10 December 2013 (UTC)