阿贝尔群G_n(P^m)的自同构群的构造

THE STRUCTURE OF THE AUTOMORPHISM GROUP OF THE ABELIAN GROUP Gn (P^m)

本文对任意的自然数n、m及素数P,讨论了具有特征■的阿贝尔群G_n(P^m)的自同构群的构造,证明了主要定理:Aut(G_n(P^m))与整环ZP^m上的几阶矩阵乘法群M_n(P^m)同构。

In the paper, we studied the automorphism groups of the Abelian group Gn(p^m), which has characteristics(P^m, P^m, …P^m), for arbi trary natural number n, m, and prime number P. The paper also Proves the chief theorem. 'Aut(Gn(P^m)) is automorphic to Mn(P^m), norder matrix group on the integral ring Zpm.