On some classes of finite quasi-F-groups

Abstract

Let G be a finite group and F a class of finite groups. We say that G is a quasi-Fgroup if for every F-eccentric chief factor H / K of G and every x ∈ G, x induces an inner automorphism on H / K. In this paper, the general theory of quasi-F -groups is given and some of its applications are considered. In particular, some characterizations of quasisoluble groups and quasisupersoluble groups are obtained.