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

Abstract

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.