非正规子群阶的个数是2的有限群  

Finite Groups with the Number of Non-Normal Subgroups of Order 2

作　　者：黄硕安 吕恒[1] HUANG Shuoan;LYU Heng(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）》2022年第10期45-49,共5页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11971391,12071376);重庆市科学创新项目(CYB20087)。

摘　　要：有限群的非正规子群的数量性质对有限群的结构有重要影响.本文设J(G)表示有限群G的非正规子群阶的个数,讨论了J(G)=2的有限群G的结构,并给出了这类有限群的分类.The numerical properties of the non-normal subgroups of a finite group have an important influence on the structure of a finite group.In this paper,let J(G) denote the number of non-normal subgroups orders of finite group G,the structure of finite group G with J(G)=2 has been discussed and the classification of the finite group been given.

关 键 词：非正规子群 可解群 幂零群 

分 类 号：O152.1[理学—数学]