摘要
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ZF∞(G/HG)中.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p幂零群的新判别准则.
Let G be a finite group and f a 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=HT and （H∩T）HG/HG is contained in the f hypercenter Z∞^f （G/HG） of G/HG. Here, f-supplemented subgroups were used to study the structure of finite groups and some new criteria of p-nilpotent groups were obtained.
基金
Supported by NNSF of China(11071229)
the Natural Science Foundation of the Jiangsu Higher Education Institutions of China(10KJD110004)
关键词
有限群
F可补充子群
p幂零群
极大子群
finite group
g-supplemented group
p-nilpotent group
maximal subgroup
