On p-nilpotency of finite groups*

Abstract

Let \( {\user1{\mathcal{F}}} \) be a class of groups. A subgroup H of a group G is called \( {\user1{\mathcal{F}}} \)-s-supplemented in G, if there exists a subgroup K of G such that G = HK and K/K ∩ HG belongs to \( {\user1{\mathcal{F}}} \) where HG is the maximal normal subgroup of G which is contained in H. The main purpose of this paper is to study some subgroups of Fitting subgroup and generalized Fitting subgroup \( {\user1{\mathcal{F}}} \)-s-supplemented and some new criterions of p-nilpotency of finite groups are obtained.