所有非交换子群皆次正规的有限群

上海大学学报(自然科学版) ›› 2009, Vol. 15 ›› Issue (1): 11-13.

所有非交换子群皆次正规的有限群

雒晓良,郭秀云

上海大学理学院,上海 200444

收稿日期:2007-06-11 出版日期:2009-02-21 发布日期:2009-02-21
通讯作者: 郭秀云
作者简介:郭秀云(1956～)，男,教授，博士生导师，博士，研究方向为有限群.
基金资助:
国家自然科学基金资助项目(10471085)；上海大学研究生创新基金资助项目

Finite Groups with Every Non-abelian Subgroup Being Subnormal

College of Sciences, Shanghai University, Shanghai 200444, China

Received:2007-06-11 Online:2009-02-21 Published:2009-02-21

摘要/Abstract

摘要：

研究了每一非交换子群皆为次正规的有限非幂零群的结构.首先证明这类群为可解群，其次通过分析Sylow子群的性质给出了这类群的一个充要条件以及一些结构性质，最后作为应用讨论具有上述性质的超可解群.

关键词: 次正规子群；A-群；非幂零群；超可解群

Abstract:

In this paper， the finite non-nilpotent group with every non-abelian subgroup being subnormal is investigated.It’s shown that such groups are solvable, and then give a necessary and sufficient condition and some structures for this kind of groups by taking into account the Sylow subgroups. As an application, the supersolvable group with the above property is discussed.

Key words: subnormal subgroup； A-group; non-nilpotent group; super-solvable group

雒晓良,郭秀云. 所有非交换子群皆次正规的有限群[J]. 上海大学学报(自然科学版), 2009, 15(1): 11-13.

LUO Xiao-liang,GUO Xiu-yun. Finite Groups with Every Non-abelian Subgroup Being Subnormal[J]. Journal of Shanghai University（Natural Science Edition）, 2009, 15(1): 11-13.