有限群的可解性与p幂零性(英文)

On solubility and p-nilpotency of finite groups

设G是一个有限群,F是一个群类.群G的子群H称为在G中是F可补充的,如果存在G的子群T使得G=HT且(H∩T)HG/HG含于G/HG的F超中心中.本文主要利用F可补充子群进一步研究群的结构,得到了一些关于可解群和p幂零群的新刻画.

Let G be a finite group and Ha class of groups. A subgroup H of G is said to be F-supplemented in G if there exists a subgroup T of G such that G= TH and （H∩ T）HG/HG is contained in the H-hypercenter ZF∞ （G/Hc） of G/HG. In this paper, we use H-supplemented subgroups to give some new characterizations of finite soluble groups and p-nilpotent groups.