Let G be a finite group and ℱ a class of finite groups. We say that G is a quasi-ℱ-group 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.
© de Gruyter 2009