超可解群的自中心化子群  

Self⁃centralizing Subgroup of Supersolvable Groups

作　　者：景瑞姣 周芳 JING Ruijiao;ZHOU Fang(School of Mathematics and Statistics,Taiyuan Normal University,Jinzhong Shanxi 030619,China)

机构地区：[1]太原师范学院数学与统计学院,山西晋中030619

出　　处：《太原师范学院学报（自然科学版）》2024年第1期24-27,共4页Journal of Taiyuan Normal University:Natural Science Edition

基　　金：山西省应用基础研究计划(自由探索类)青年项目(202103021223328).

摘　　要：自中心化子群是一种重要的子群,称H是有限群G的自中心化子群,若H≤G,满足CG(H)≤H.当有限群G为p-群或者幂零群时,其极大交换正规子群是自中心化子群,我们将该结果推广到有限超可解群上.作为应用,计算了16阶群G=〈a,b|a8=1,b2=a4,b-1ab=a-1〉的自中心化子群,并给出了反例说明该结果在可解群G=SL(2,3)上不是普遍成立的.The self-centralizing subgroup is an important subgroup which is called H as the self-centralizing subgroup of the finite group G,if H≤G,satisfies CG(H)≤H.When a finite group G is a p⁃group or a nilpotent group,its maximal abelian normal subgroup is a self-centralizing subgroup.This result can be extended to finite supersolvable groups.As an application,we calculate a self-centralizing subgroup of order 16 G=a,b|a8=1,b2=a4,b-1 ab=a-1 and give an untenable counterexample on a solvable group G=SL(2,3).

关 键 词：超可解群 极大交换正规子群 自中心化子群 

分 类 号：O211.5[理学—概率论与数理统计]