有限群的F_n-可补子群

On p-nilpotency of finite groups of F_n-supplemented subgroup

设F是一个群类,如果存在群G的正规子群K满足G=HK且(H∩K)HG/HG包含在G/HG的F-超中心Z∞F(G/HG)中,则称群G的子群H在G中Fn-可补.利用准素子群的Fn-可补性研究有限群的结构,得到p-幂零群的一些条件.

Let G be a finite group and F a formation of finite groups.A subgroup Hof G is called Fn-supplemented in G if there exists a normal subgroup K of G such that G=HK and（H∩K）HG/HG is contained in the F-hypercenter Z∞F（G/HG） of G/HG.The author studies the structure of finite groups with Fn-supplemented primary subgroup and gets some condition for p-nilpotent of group G.