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Finite Groups in Which Sylow 2-Subgroups are Abelian and Centralizers of Involutions are Solvable

Published online by Cambridge University Press:  20 November 2018

Daniel Gorenstein
Daniel Gorenstein*
Affiliation:
Clark University, Worcester, Massachusetts
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The purpose of this paper is to establish the following theorem :

Theorem 1. Let be a finite group with abelian Sylow 2-subgroups in which the centralizer of every involution is solvable. Then either is solvable or else /O is isomorphic to a subgroup of PΓL(2, q) containing PSL(2, q), where either q = 3 or 5 (mod 8), q ≥ 5, or q = 2n, n ≥ 2.

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 17 , 1965 , pp. 860 - 906
Copyright
Copyright © Canadian Mathematical Society 1965

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