有限阶Abelian群同构类的计算

The Calculation of the Isomorphism Classes of a Finite Abelian Group

该文通过运用组合数学中整数分拆的知识,结合有限Abelian群的基本结构定理,给出了有限阶Abelian群的同构类的计算公式,使得对于所给的任意有限阶Abelian群,都可以通过该公式计算出它的同构群的种类,最后,作者把该方法在计算机上实现,尤其是当阶数取得很大并且已超越人脑计算时,这将使计算更加容易和便利.

In this paper, the author give a computational formula to calculate the isomorphism classes of a fi- nite abelian group, by using the partition theory of integers in combinatorics and the fundamental structure theorem of finite abelian groups, so that one could determine easily the isomorphism classes of any finite abelian group once its order is given. In the last, she also implement the method on computer, which will make the computation much easier and facilitater, especially when the order gets larger and beyond head computation.