超可解群的自中心化子群
Self-centralizing Subgroup of Supersolvable Groups
景瑞姣 1周芳1
作者信息
- 1. 太原师范学院数学与统计学院,山西晋中 030619
- 折叠
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=a1>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.
Abstract
The self-centralizing subgroup is an important subgroup which is called H as the self-centralizing subgroup of the finite group G,ifH≤G,satisfies CG(H)≤ H.When a finite group G is ap-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-1ab=a-1>and give an untenable coun-terexample 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Key words
supersolvable groups/maximal abelian normal subgroups/self-centralizing sub-group引用本文复制引用
基金项目
山西省应用基础研究计划(自由探索类)青年项目(202103021223328)
出版年
2024
NETL
NSTL
万方数据