Finite groups whose maximal subgroups have the hall property

Abstract

We study the structure of finite groups whosemaximal subgroups have the Hall property. We prove that such a group G has at most one non-Abelian composition factor, the solvable radical S(G) admits a Sylow series, the action of G on sections of this series is irreducible, the series is invariant with respect to this action, and the quotient group G/S(G) is either trivial or isomorphic to PSL2(7), PSL2(11), or PSL5(2). As a corollary, we show that every maximal subgroup of G is complemented. © 2013 Allerton Press, Inc.