In mathematical finite group theory, the GorensteinâHarada theorem, proved by Daniel Gorenstein and Koichiro Harada, classifies the simple finite groups of sectional 2-rank at most 4. [1] [2] It is part of the classification of finite simple groups. [3]
Finite simple groups of section 2 with rank at least 5 have Sylow 2-subgroups with a self-centralizing normal subgroup of rank at least 3, which implies that they have to be of either component type or of characteristic 2 type. Therefore, the GorensteinâHarada theorem splits the problem of classifying finite simple groups into these two sub-cases.
References
- ^ Gorenstein, D.; Harada, Koichiro (1973). "Finite groups of sectional 2-rank at most 4". In Gagen, Terrence; Hale, Mark P. Jr.; Shult, Ernest E. (eds.). Finite groups '72. Proceedings of the Gainesville Conference on Finite Groups, March 23-24, 1972. North-Holland Math. Studies. Vol. 7. Amsterdam: North-Holland. pp. 57â67. ISBN 978-0-444-10451-9. MR 0352243.
- ^ Gorenstein, D.; Harada, Koichiro (1974). Finite groups whose 2-subgroups are generated by at most 4 elements. Memoirs of the American Mathematical Society. Vol. 147. Providence, R.I.: American Mathematical Society. ISBN 978-0-8218-1847-3. MR 0367048.
- ^ Bob Oliver (25 January 2016). Reduced Fusion Systems over 2-Groups of Sectional Rank at Most 4. American Mathematical Society. pp. 1, 3. ISBN 978-1-4704-1548-8.
 | This algebra-related article is a stub. You can help Wikipedia by expanding it. |
In mathematical finite group theory, the GorensteinâHarada theorem, proved by Daniel Gorenstein and Koichiro Harada, classifies the simple finite groups of sectional 2-rank at most 4. [1] [2] It is part of the classification of finite simple groups. [3]
Finite simple groups of section 2 with rank at least 5 have Sylow 2-subgroups with a self-centralizing normal subgroup of rank at least 3, which implies that they have to be of either component type or of characteristic 2 type. Therefore, the GorensteinâHarada theorem splits the problem of classifying finite simple groups into these two sub-cases.
References
- ^ Gorenstein, D.; Harada, Koichiro (1973). "Finite groups of sectional 2-rank at most 4". In Gagen, Terrence; Hale, Mark P. Jr.; Shult, Ernest E. (eds.). Finite groups '72. Proceedings of the Gainesville Conference on Finite Groups, March 23-24, 1972. North-Holland Math. Studies. Vol. 7. Amsterdam: North-Holland. pp. 57â67. ISBN 978-0-444-10451-9. MR 0352243.
- ^ Gorenstein, D.; Harada, Koichiro (1974). Finite groups whose 2-subgroups are generated by at most 4 elements. Memoirs of the American Mathematical Society. Vol. 147. Providence, R.I.: American Mathematical Society. ISBN 978-0-8218-1847-3. MR 0367048.
- ^ Bob Oliver (25 January 2016). Reduced Fusion Systems over 2-Groups of Sectional Rank at Most 4. American Mathematical Society. pp. 1, 3. ISBN 978-1-4704-1548-8.
|
| This algebra-related article is a stub. You can help Wikipedia by expanding it. |