所有非交换子群皆次正规的有限群  

Finite Groups with Every Non-abelian Subgroup Being Subnormal

作　　者：雒晓良[1] 郭秀云[1] 

机构地区：[1]上海大学理学院,上海200444

出　　处：《上海大学学报（自然科学版）》2009年第1期11-13,共3页Journal of Shanghai University:Natural Science Edition

基　　金：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

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.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.

关 键 词：次正规子群 A-群 非幂零群 超可解群 

分 类 号：O152.1[理学—数学]