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

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。

Abstract: 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.