子群与不变子群的充要条件

Sufficient and Necessary Conditions of Subgroups and Invariant Subgroups

本文介绍子群的两个充要条件。利用这两个子群的充要条件求出群S3的全部子群,模十二的剩余类加群的所有子群,以及子群的陪集的求解方法与技巧。进而利用子群来推测整个群的性质,所以子群对于研究整个群论有着必不可少的作用。

This paper introduces two sufficient and necessary conditions of subgroups.All subgroups of the group S3 and the residual classes plus group with module 12 will be foundusing the sufficient and necessary conditions of the subgroups,and the solving methods and techniques for the cosets of the subgroups will be proposed.Then subgroups are used to predict the properties of the whole group.Therefor the subgroups play an essential role in the study on the whole group theory.