6元群数量的四种证法

The Four Solutions of the Structure of 6 Elements Group

阶数小于6的群的类型,我们很容易搞清楚,除了四元群有两种不同的类型即循环群和克莱因四元群外,1,2,3,5阶群都是循环群,都各有一种,那么6元群有几种呢?这个问题的回答并非一目了然.本文给出四种证法,证明6元群也只有两种,即循环群和三次对称群S3.

In this paper, We will discuss the number of 6 elements group in view of isomorphism. In term of the propoties of group, we can prove that 6 elements group have two distinct groups,, namely, cyclic group and symmetric group on 3 letters, S3 Furthermore, we present four different ways to verify this point.