恰有10个非正规子群的有限幂零群  

On Finite Nilpotent Groups Having Exactly Ten Non-Normal Subgroups

作　　者：范睿 陈贵云[1] FAN Rui;CHEN Gui-yun(School of Mathematics and Statistics,Southwest University,Chongqing 400715,China)

机构地区：[1]西南大学数学与统计学院,重庆400715

出　　处：《西南师范大学学报（自然科学版）》2018年第10期5-8,共4页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11671324)

摘　　要：一直以来,利用子群和商群来刻画有限群的结构是一个热门话题.通过研究正规子群的性质来讨论有限群的结构是群论研究中一个非常重要的课题,在这方面已经取得了许多丰富和重要的结果.讨论其对偶问题,也就是非正规子群的性质对有限群结构的影响.基于非正规子群的共轭类类数为4,5的有限幂零群的结构,运用局部分析的方法,给出恰含10个非正规子群的有限幂零群的完全分类.为恰有2p个非正规子群的有限群的研究开拓了思路.It has been a topic to use subgroups and quotient groups to describe the structures of finite groups.The discussion of the structure of finite groups by studying the properties of normal subgroups is a very important topic in group theory research.Many rich and important results have been obtained.Here It is discussed the dual problem,which is the effect of the nature of the non-normal subgroup on the finite group structure.Using the structure of finite nilpotent groups whose four and five conjugate classes of non-normal subgroups.It is classified that all finite nilpotent groups having exactly ten non-normal subgroups by applying the local analysis methods.The result develop the research idea of finite group with 2p non-normal subgroups.

关 键 词：有限幂零群 非正规子群 个数 分类 

分 类 号：O152.1[理学—数学]