On Fs -supplemented primary subgroups of finite groups

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