C_p^n×C_p^m(n>m,p为素数）的自同构群

The automorphism groups of C_p^n×C_p^m(n>m,pis a prime number)

目的确定C_p^n×C_p^m(n>m,p为素数)的自同构群的阶及结构。方法根据自同构群及循环群的性质定理,利用模n的原根存在性,确定C_p^n×C_p^m(n>m,p为素数)的自同构群的阶及它的生成元。结果与结论得到自同构群的阶,并确定了C_p^n×C_p^m(n>m,p>2)的自同构群的结构。

Purposes-To determine the order and structure of the automorphism groups of C_p^n×C_p^m(n>m,pis a prime number).Methods-According to the theorem of automorphism group and cyclic group,the order of automorphism group of C_p^n×C_p^m(n>m,pis a prime number)and its generator are determined by the existence of the primitive root of the module n.Result and Conclusion-The order of the automorphism group is obtained and the structure of the automorphism groups of C_p^n×C_p^m(n>m,p >2)is determined.