关于循环子群数目超过一半的几乎单群
ALMOST SIMPLE GROUPS WITH MORE THAN HALF NUMBER OF CYCLIC SUBGROUPS
徐卫东 1沈如林1
作者信息
- 1. 湖北民族大学数学与统计学院,湖北,恩施 445000
- 折叠
摘要
假设G为有限群,记c(G)为群G的循环子群个数,α(G)为群G的循环子群个数与群阶数的比值,即α(G):=c(G)/|G|.本次研究证明了若G为几乎单群,即S≤G≤Aut(S),这里S为有限非交换单群,则α(G)≥1/2当且仅当G≌A5,S5,S6.
Abstract
Let G be a finite group,c(G)be the number of cyclic subgroups of G,and α(G)be the ratio of the number of cyclic subgroups of G to the order of the group,i.e.α(G):= c(G)/|G|.In this paper,it proves that if G is an almost simple group,i.e.S≤G≤Aut(S),in which S is a finite non-abelian simple group,then α(G)≥1/2 if and only if G≌A5,S5,S6.
关键词
有限群/几乎单群/循环子群个数Key words
finite groups/almost simple groups/number of cyclic subgroups引用本文复制引用
出版年
2024
国家科技期刊平台
NSTL
维普
万方数据