由一道习题谈子群的乘积是子群的判定条件  

The Subgroup’s Judgment Conditions Based on Subgroup Product from an Exercise

作　　者：孙倩 廖小莲[1] 

机构地区：[1]湖南人文科技学院数学系,湖南娄底

出　　处：《理论数学》2019年第4期546-550,共5页Pure Mathematics

摘　　要：由于有限群G的子群的乘积不一定是G的子群,如何判断子群的乘积为子群是一个值得探讨的问题。我们将从一道课后习题出发,来探索有限群的子群的乘积是子群的判定条件,重点推导一个群的两个子群的乘积是子群的判断条件,并将子群个数推广到三个的情形。Since the product of a subgroup of a finite group G is not necessarily a subgroup of G,how to judge the product of a subgroup as a subgroup is a question worthy of discussion.Starting from an after-class exercise,we will explore that the product of two subgroups of a finite group is the judgment condition of the subgroup,mainly deduce that the product of two subgroups of a group is the judgment condition of the subgroup,and generalize the number of groups to three cases.

关 键 词：群 子群 不变子群 子群的乘积 

分 类 号：O1[理学—数学]