自中心化子群的s-正规性对有限群结构的影响  

The influence of s-normality of self-centralizing subgroups on the structure of finite groups

作　　者：陈婵婵 卢家宽 CHEN Chanchan;LU Jiakuan(School of Mathematics and Statistics,Guangxi Normal University,Guilin 541004,China)

机构地区：[1]广西师范大学数学与统计学院,广西桂林541004

出　　处：《湘潭大学学报（自然科学版）》2022年第2期58-62,共5页Journal of Xiangtan University(Natural Science Edition)

基　　金：国家自然科学基金(11861015)。

摘　　要：该文主要研究自中心化子群的s-正规性对有限群结构的影响,证明:每个自中心化子群都是s-正规子群的有限群可解.进一步研究了Sylow子群极小子群的s-正规自中心化对有限群结构的影响,证明:如果有限群G的Sylowp-子群P的每个极小子群是G的s-正规自中心化子群且Op(G)=1,则G是p-幂零群.进一步证明:若G的p阶子群是G的s-正规自中心化子群且Φ(G)=1,其中(G,p-1)=1,则G是p-幂零群.In this paper,we mainly study the influence of s-normality of self-centralizing subgroups on the structure of finite groups,and prove that if every self-centralizing subgroup of finite group Gis s-normal subgroup,then Gis solvable.We further study the influence of s-normal self-centralization of minimum subgroups of Sylow subgroups on the structure of finite groups,and obtain that if every minimum subgroup of Sylowp-subgroup of finite group Gis s-normal self-centralizing subgroup of Gand Op(G)=1,then Gis p-nilpotent.We further prove that if every p order subgroup of finite group Gis s-normal self-centralizing subgroup of GandΦ(G)=1,where the order of finite group Gis coprime with p-1,then Gis p-nilpotent.

关 键 词：自中心化 s-正规 P-幂零群 可解群 

分 类 号：O152.1[理学—数学]