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

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.