On $F_s$ -supplemented primary subgroups of finite groups

Abstract

Let G be a finite group and F a formation of finite groups. A subgroup H of G is called $F_s$-supplemented in G if there exists a subnormal subgroup T of G such that G = HT and (H ∩ T)$H_G/H_G$ is contained in the F-hypercenter $Z^F_infty$ (G/HG) of $G/H_G$ . In this paper, we study the structure of finite groups by using $F_s$-supplemented subgroups.