Abel群的一个新刻划

A New Characteristic of Abel Group

Serre利用群的特征标理论给出了有限群是Abel群的一个充要条件,该文利用群的表示理论给出了无限群是有限生成Abel群的一个新刻划,且对Serre关于有限Abel群的定理给出了一个新的证明。

Serre had given one necessary and sufficient condition of finite group being a A-bel group through the character theory of group. In this paper,a new characteristic of a infinite Abel group with finite generators,and a new proof of the finite Abel group theorem were given.