所有极大子群都为SMSN-群的有限群（英文）  

FINITE GROUPS WHOSE ALL MAXIMAL SUBGROUPS ARE SMSN-GROUPS

作　　者：郭鹏飞[1,2] GUO Peng-fei(School of Mathematics and Statistics, Hainan Normal University, Haikou 571158, China;School of Mathematics and Information Engneering, Lianyungang Normal College,Lianyungang 222006, China)

机构地区：[1]海南师范大学数学与统计学院,海南海口571158 [2]连云港师范高等专科学校数学与信息工程学院,江苏连云港222006

出　　处：《数学杂志》2017年第4期714-722,共9页Journal of Mathematics

基　　金：Supported by National Natural Science Foundation of China(11661031);Jiangsu Overseas Research&Training Program for University Prominent Young & Middle-Aged Teachers and Presidents;"333" Project of Jiangsu Province(BRA2015137);"521" Project of Lianyungang City

摘　　要：若有限群G的每个2-极大子群在G中次正规,则称G为SMSN-群.本文研究了有限群G的每个真子群是SMSN-群但G本身不是SMSN-群的结构,利用局部分析的方法,获得了这类群的完整分类,推广了有限群结构理论的一些成果.Aˉnite group G is called an SMSN-group if its2-maximal subgroups are sub-normal in G.In this paper,the author investigates the structure ofˉnite groups which are not SMSN-groups but all their proper subgroups are SMSN-groups.Using the idea of local analysis,a complete classiˉcation of this kind of groups is given,which generalizes some results of the structure ofˉnite groups.

关 键 词：幂自同构 幂零群 内幂零群 极小非SMSN-群 

分 类 号：O152.1[理学—数学]