Finite groups with a proper 2-generated core

Aschbacher, Michael

doi:10.1090/S0002-9947-1974-0364427-8

Finite groups with a proper $2$-generated core
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by Michael Aschbacher

Trans. Amer. Math. Soc. 197 (1974), 87-112

DOI: https://doi.org/10.1090/S0002-9947-1974-0364427-8

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Abstract:

H. Bender’s classification of finite groups with a strongly embedded subgroup is an important tool in the study of finite simple groups. This paper proves two theorems which classify finite groups containing subgroups with similar but somewhat weaker embedding properties. The first theorem, classifying the groups of the title, is useful in connection with signalizer functor theory. The second theorem classifies a certain subclass of the class of finite groups possessing a permutation representation in which some involution fixes a unique point.

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