On partial CAP∗-subgroups of finite groups

Abstract

A subgroup [Formula: see text] of a finite group [Formula: see text] is said to be a partial [Formula: see text]-subgroup of [Formula: see text] if there exists a chief series [Formula: see text] of [Formula: see text] such that [Formula: see text] either covers or avoids each non-Frattini chief factor of [Formula: see text]. In this paper, we study the influence of the partial [Formula: see text]-subgroups on the structure of finite groups. Some new characterizations of the hypercyclically embedded subgroups, [Formula: see text]-nilpotency and supersolubility of finite groups are obtained.