用交换子群的个数刻画A5和S5  

Characterizing A5 and S5 by the Numbers of Its Abelian Subgroups

作　　者：钱焱 陈贵云[1] QIAN Yan;CHEN Gui-yun(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：《西南师范大学学报（自然科学版）》2020年第6期5-8,共4页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11671324)。

摘　　要：利用完全初等的方法刻画交错群A5和对称群S5.得到如下结论:若群G的阶为60,则G≌A5的充要条件是G的交换子群的阶为2,3,4,5,且个数分别是15,10,5,6;若群G的阶为120,则G≌S5的充要条件是G的交换子群的阶为2,3,4,5,6,且个数分别是25,10,35,6,10.It is proved that A5 and S5 can be uniquely determined by its order and the numbers of its abelian subgroups of different orders by elementary approaches.The conclusions are as following:If the order of group G is 60,then G≌A5 if and only if the orders of the abelian subgroups of G are 2,3,4,5 and the numbers of them are 15,10,5,6 respectively;If the order of group G is 120,then G≌S5 if and only if the orders of the abelian subgroups of G are 2,3,4,5,6,and the numbers of them are 25,10,35,6,10 respectively.

关 键 词：群的阶 交换子群 群的结构 

分 类 号：O152.1[理学—数学]