Gorenstein–Harada theorem

In mathematical finite group theory, the Gorenstein–Harada 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 Gorenstein–Harada theorem splits the problem of classifying finite simple groups into these two sub-cases.

References

  1. ^ 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. 57–67. ISBN 978-0-444-10451-9. MR 0352243.
  2. ^ 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.
  3. ^ 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.


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