同阶交换子群个数之集为{1,3}的有限群  

Finite Groups Whose Set of the Number of Abelian Subgroups of the Same Order Is{1,3}

作　　者：钱焱 陈贵云[1] QIAN Yan;CHEN Guiyun(School of Mathematics and Statistics,Southwest University,Chongqing 400715,China)

机构地区：[1]西南大学数学与统计学院,重庆400715

出　　处：《西南大学学报（自然科学版）》2021年第10期100-104,共5页Journal of Southwest University(Natural Science Edition)

基　　金：国家自然科学基金项目(12071376).

摘　　要：证明了不存在同阶交换子群个数之集为{1,2}的有限群,并且完全确定了同阶交换子群个数之集为{1,3}的有限群结构.作为推论,得到:群G的同阶交换子群个数之集为{1,3}等价于群G的同阶子群个数之集为{1,3}.It is proved in this paper that there is no finite group G satisfying the condition that the set of the number of abelian subgroups of the same order is{1,2}.Furthermore,it is determined that the structure of the finite group G whose set of the number of abelian subgroups of the same order is{1,3}.It is,hence,derived that for a group G,the set of the number of abelian subgroups of the possible order is{1,3}if and only if the set of the number of subgroups of the possible order is{1,3}.

关 键 词：同阶交换子群 阶 群结构 

分 类 号：O152.1[理学—数学]