Finite Groups with Some Self-Conjugate-Permutable Subgroups
Received:April 08, 2023  Revised:January 06, 2024
Key Words: $SC$-group   $PSC$-group   self-conjugate-permutable subgroup   maximal subgroup  
Fund Project:Supported by the National Natural Science Foundation of China (Grant No.12061030) and the Natural Science Foundation of Hainan Province (Grant No.122RC652).
Author NameAffiliation
Wanlin WANG School of Mathematics and Statistics, Hainan Normal University, Hainan 571158, P. R. China 
Pengfei GUO School of Mathematics and Statistics, Hainan Normal University, Hainan 571158, P. R. China 
Hits: 84
Download times: 98
Abstract:
      A subgroup $H$ of a group $G$ is said to be self-conjugate-permutable if $HH^{x}=H^{x}H$ implies $H^{x}=H$ for any $x$ of $G$. A finite group $G$ is called an $SC$-group ($PSC$-group, respectively) if all cyclic subgroups of $G$ of order $2$ or order $4$ (prime order or order $4$, respectively) are self-conjugate-permutable in $G$. In this paper, we first investigate the structure of finite non-solvable groups all of whose second maximal subgroups are $SC$-groups; then we mainly investigate the structure of finite groups in which all of maximal subgroups of even order are $PSC$-groups. In fact, we describe the structure of finite groups which are not $PSC$-groups but all of whose maximal subgroups of even order are $PSC$-groups.
Citation:
DOI:10.3770/j.issn:2095-2651.2024.02.006
View Full Text  View/Add Comment