On weakly c-supplemented subgroups of finite groups

Abstract

Let [Formula: see text] be a finite group. If [Formula: see text] is a subgroup of [Formula: see text] and [Formula: see text] a subgroup of [Formula: see text], we say that [Formula: see text] is strongly closed in [Formula: see text] with respect to [Formula: see text] if [Formula: see text] for any [Formula: see text]. We say that a subgroup [Formula: see text] of [Formula: see text] is strongly closed in [Formula: see text] if [Formula: see text] is strongly closed in [Formula: see text] with respect to [Formula: see text]. A subgroup [Formula: see text] of a group [Formula: see text] is said to be weakly [Formula: see text]-supplemented in [Formula: see text] if [Formula: see text] has a subgroup [Formula: see text] such that [Formula: see text] and [Formula: see text] is strongly closed in [Formula: see text]. In this paper, we study the structure of a group [Formula: see text] under the assumption, that some subgroups of prime power order are weakly [Formula: see text]-supplemented in [Formula: see text]. Our results extend and generalize several recent results in the literature.