p幂零群的新判别准则

摘要

设G是一个有限群,(￡)是一个群类.群G的子群H称为在G中是(￡)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(￡)超中心(￡)(G/HG)中.主要利用(￡)可补充子群进一步研究群的结构,得到了一些关于p幂零群的新判别准则.%Let G be a finite group and (￡)a class of groups.A subgroup H of G is said to be (￡)-supplemented in G if there exists a subgroup T of G such that G=HT and (H ∩ T) HG/HG is contained in the (￡)-hypercenter Z(￡)∞ (G/HG) of G/HG.Here,(￡)-supplemented subgroups were used to study the structure of finite groups and some new criteria of p-nilpotent groups were obtained.