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

作　　者：徐卫东 沈如林 XU Weidong;SHEN Rulin(School of Mathematics and Statistics,Hubei Minzu University,Enshi,Hubei 445000,China)

机构地区：[1]湖北民族大学数学与统计学院,湖北恩施445000

出　　处：《井冈山大学学报（自然科学版）》2024年第2期7-11,共5页Journal of Jinggangshan University (Natural Science)

基　　金：国家自然科学基金项目(12161035)。

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a(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■@A_(5),S_(5),S_(6)。Let G be a finite group,c(G)be the number of cyclic subgroups of G,andα(G)be the ratio of the number of cyclic subgroups of G to the order of the group,i.e.a(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,thenα(G)≥1/2if and only if G■@A_(5),S_(5),S_(6).

关 键 词：有限群 几乎单群 循环子群个数 

分 类 号：O152.1[理学—数学]