关于F-可补子群的一个注记

A Note on F-supplemented Subgroup

设G是一个有限群,F是一个群系,称群G的一个子群H在G中F-可补的,如果存在G的一个子群T,使得G=HT且(H∩T)HG/HG包含在G/HG的F-超中心ZF∞(G/HG),利用F-可补子群研究有限群的p-幂零性,推广和统一了一些已知的结果。

Let G be a finite group and F a formation of finite groups.A subgroup H of G is F-supplemented in G if there exists a 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 use F-supplemented subgroups to study p-nilpotency of finite groups.A series of previously known results are unified and generalized.