Finite Groups with Some Self-Conjugate-Permutable Subgroups

作     者：Wanlin WANG Pengfei GUO Wanlin WANG;Pengfei GUO

作者机构：School of Mathematics and Statistics Hainan Normal University 

出 版 物：《Journal of Mathematical Research with Applications》 (数学研究及应用(英文))

年 卷 期：2024年第44卷第2期

页      面：199-208页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：Supported by the National Natural Science Foundation of China (Grant No. 12061030) the Natural Science Foundation of Hainan Province (Grant No. 122RC652) 

主　　题：SC-group PSC-group self-conjugate-permutable subgroup maximal subgroup 

摘      要：A subgroup H of a group G is said to be self-conjugate-permutable if H Hx= HxH implies Hx= H for any x of G. A finite group G is called an SC-group(P SC-group, respectively)if all cyclic subgroups of G of order 2 or order 4(prime order or order 4, respectively) are selfconjugate-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 P *** fact, we describe the structure of finite groups which are not P SC-groups but all of whose maximal subgroups of even order are P SC-groups.