某些素数幂阶子群可补的有限群

上海大学学报(自然科学版) ›› 2009, Vol. 15 ›› Issue (4): 369-374.

某些素数幂阶子群可补的有限群

郭孝军郭秀云

上海大学理学院，上海 200444

收稿日期:2008-03-19 出版日期:2009-08-30 发布日期:2009-08-30
通讯作者: 郭秀云(1956～)，男，教授，博士生导师,博士,研究方向为有限群. E-mail:xyguo@staff.shu.edu.cn
基金资助:
国家自然科学基金资助项目(10771132);上海大学创新基金资助项目

Finite Groups with Some Complemented Subgroups of Prime Power Order

College of Sciences, Shanghai University, Shanghai 200444, China

Received:2008-03-19 Online:2009-08-30 Published:2009-08-30

摘要/Abstract

摘要：

有限群G的子群H称为在G中是可补的，如果存在G的子群K，使得G=HK且H∩K=1. 利用群G的某些极小子群及素数幂阶子群在G可补，给出群G的一些性质和结构. 

关键词: 可补子群；极小子群；超可解群；p-幂零群

Abstract:

A subgroup H of a finite group G is said to be complemented in G if there exists a subgroup K of G such that G =HK and H∩K=1. In this paper, new results of the structure and properties of a finite group G are given, provided some minimal subgroups and subgroups of prime power order are complemented in G.

Key words: complemented subgroup; minimal subgroup; supersolvable group; p-nilpotent group

中图分类号:

O152.1

郭孝军郭秀云. 某些素数幂阶子群可补的有限群[J]. 上海大学学报(自然科学版), 2009, 15(4): 369-374.

GUO Xiao-Jun, GUO Xiu-Yun. Finite Groups with Some Complemented Subgroups of Prime Power Order[J]. Journal of Shanghai University（Natural Science Edition）, 2009, 15(4): 369-374.