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Finite Groups With a Proper 2-Generated Core

Michael Aschbacher
Transactions of the American Mathematical Society
Vol. 197 (Oct., 1974), pp. 87-112
DOI: 10.2307/1996929
Stable URL: http://www.jstor.org/stable/1996929
Page Count: 26
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Finite Groups With a Proper 2-Generated Core
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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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