On F<sub>τ</sub>-s-supplemented Subgroups of Finite Groups

Abstract

Let F be a non-empty formation of groups, τ a subgroup functor and H a p-subgroup of a finite group G. Let Ḡ=G/HG and H = H/HG. We say that H is Fτs-supplemented in G if for some subgroup T and some τ-subgroup S of Ḡ contained in H, HT is subnormal in Ḡ and H∩ T ≤ SZF(Ḡ). In this paper, we investigate the influence of Fτ-s-supplemented subgroups on the structure of finite groups. Some new characterizations about solubility of finite groups are obtained. AMS subject classifications: 20D10, 20D15, 20D20