S_3的一个特征性质

A CHARACTERISTIC PROPERTY OF S_3

S_3是阶最小的非交换群,人们对它已有各式各样的刻划,这篇短文也给出S_3的一种刻划:定理 任何非交换群G同构于S_3,当且仅当G具有性质:若任意a,b∈G,当a≠b,ab=ba时,则有a=1,或b=1,或ab=1.

In this paper, Any non-commuta tive group G is isomorphic to S3, if and only if G possesses the proporfy: for any a b∈G, a=b, ab = ba a = 1, or b = 1, or ab = 1.