有限阿贝尔群的所有不可约忠实表示

All Irreducible Faithful Representations of the Finite Abelian Group

令C为复数域，G为有限群。由于每个CG-模可以写成不可约CG-模的直和，于是对表示的研究实际转化成了对不可约表示的研究。而群的忠实表示可以比较好地体现原有群的性质，所以，对于给定的群，找出该群所有不可约忠实表示是很有意义的。而对于一般有限群来说，找出其所有不可约忠实表示并不容易。本文我们给出了有限阿贝尔群G的所有不可约忠实表示。

Let C be the complex field, G be a finite group. Every CG - module can be written as a direct sum of irreducible CG - modules, so it allows us just to concentrate on the irreducible representation. Moreover, it is known that the faithful representation of a group can reveal important properties of the group. Therefore, it is meaningful to obtain all irreducible faithful representations. However, it is not easy to get all irreducible faithful representations in general. For all finite abelian groups G, we give all irreducible faithful representations of G in this paper.