有限Abel群的同构定理

一、引言 设G和G′是有限群,G与G′同构与否显然是可以判定的。事实上,若G与G′都是n元有限群,则最坏的情况,要检测G与G′元素之间的n!个1—1映射。对这个问题的处理,文献1]给出了一个一般方法。 这个方法首先注意到,如果,则必然有G与G′所含周期相同的元素数目相一

The Isomorphic Theorem of Finite Abel Group

In this paper we proved that finite Abel groups G and G' are isomorphic, if they have the same numder of elements whose period was equal, this is, if in G the number of elements whose period is l is m, then in G' the number of elements whoes period is l is also m, vice versa.According to this theorem, we can efficiently determined whether finite Abel groaps G and G' are isomorphic or not.