自中心化子群对有限群结构的影响  

Influence of Self-centralizing Subgroups on the Structure of Finite Groups

作　　者：孙雨晴 卢家宽 SUN Yuqing;LU Jiakuan(College of Mathematics and Statistics, Guangxi Normal University, Guilin Guangxi, 541006, China)

机构地区：[1]广西师范大学数学与统计学院,广西桂林541006

出　　处：《广西师范大学学报（自然科学版）》2020年第5期48-55,共8页Journal of Guangxi Normal University:Natural Science Edition

基　　金：国家自然科学基金(11861015);广西高校中青年教师基础能力提升项目(2018KY0087);广西研究生教育创新计划(XYCSZ2019086,JGY2019003);广西师范大学教师成长基金(EDF2018014)。

摘　　要：本文主要研究自中心化子群的C-正规性和自中心化子群的共轭类个数对有限群结构的影响,得到了有限群为可解群、超可解群的若干充分条件,以及满足某些条件的有限群的分类。This paper mainly studies the influence of C-normality of self-centralizing subgroups and the number of conjugate classes of self-centralizing subgroups on the structure of finite groups.Some sufficient conditions for finite groups to be supersolvable groups or solvable groups are obtained and some results of the classification of finite groups certain some conditions are also obtained.

关 键 词：自中心化子群 C-正规子群 极大交换子群 可解群 

分 类 号：O152.1[理学—数学]