摘要
H是有限群G的子群,如果存在G的正规子群T,使得G=HT且H^(g)∩N_(T)(H)≤H对任意g∈G都成立,则称H为G的HC-子群.本文研究了Sylow子群的极大子群是局部子群的HC子群时群的结构,给出了有限群为p幂零群以及超可解群的一些条件.
A subgroup H of a finite group G is called an HC-subgroup of G if there exists a normal subgroup T of G such that G=HT and H^(g)∩N_(T)(H)≤H for all g∈G.In this paper,the structure of finite groups has been investigated based on assumption that all maximal subgroups of Sylow subgroups are HC-subgroups in local subgroup,and give some conditions for finite groups to be p-nilpotent and supersolvable.
作者
周红
刘建军
ZHOU Hong;LIU Jianjun(School of Mathematics and Statistics, Southwest University, Chongqing 400715, China)
出处
《西南师范大学学报（自然科学版）》
CAS
2022年第2期7-10,共4页
Journal of Southwest China Normal University(Natural Science Edition)
基金
国家自然科学基金项目(11301426)
中央高校基本科研业务费项目(XDJK2020B052)
西南大学教改项目(2019JY096).
关键词
HC子群
p幂零群
超可解群
饱和群系
HC-subgroups
p-nilpotent groups
supersolvable groups
saturated formations
