非幂零自中心化子群是TI-子群或次正规子群的有限群  

Finite Groups in Which Every Non-Nilpotent Self-Centralizing Subgroup Is a TI-Subgroup or A Subnormal Subgroup

作　　者：陈婵婵 李玉 卢家宽 张博儒 CHEN Chanchan;LI Yu;LU Jiakuan;ZHANG Boru(School of Mathematics and Statistics, Guangxi Normal University, Guilin Guangxi 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：《西南师范大学学报（自然科学版）》2021年第10期5-9,共5页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11861015);广西高校中青年教师基础能力提升项目(20210KY1597,2020KY2019);广西师范大学硕士研究生创新项目(XYCSZ20211011).

摘　　要：本文给出了所有非幂零自中心化子群是特殊子群的有限群的一些性质.证明了:如果有限群G的每个非幂零自中心化子群是TI-子群或次正规子群,则G的每个非幂零子群皆次正规于G.进一步还证明了:如果K是非幂零群G的任一非幂零自中心化子群,且K_G,或存在子群L正规于G使得L是以极大子群K为Frobenius补的Frobenius群,则G的所有非幂零自中心化子群是TI-子群.In this paper,we have obtained some properties of a finite group in which every non-nilpotent self-centralizing subgroup is a special subgroup.It has been proved that if every non-nilpotent self-centralizing subgroup of a finite group G is a TI-subgroup or a subnormal subgroup of G,then every non-nilpotent subgroup of G must be subnormal in G.We further prove that K is a non-nilpotent self-centralizing subgroup of a non-nilpotent group G,if K normal in G or exists a normal subgroup L of G such that K is a maximal subgroup of L and K is a Frobenius complement of L,then every non-nilpotent self-centralizing subgroup of G is a TI-subgroup.

关 键 词：非幂零群 自中心化子群 TI-子群 次正规子群 非循环子群 

分 类 号：O152.1[理学—数学]