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)

作　　者：范爱琴 FAN Ai-qin(Department of Mathematics and Computer,Yuncheng Advanced Normal College,Yuncheng 044000,Shanxi,China)

机构地区：[1]运城师范高等专科学校数计系

出　　处：《宝鸡文理学院学报（自然科学版）》2019年第4期24-28,共5页Journal of Baoji University of Arts and Sciences(Natural Science Edition)

基　　金：国家自然科学基金(10671114);山西省自然科学基金(2008012001)

摘　　要：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.

关 键 词：自同构群 模 循环群 生成元 阶 自同构群的结构 

分 类 号：O152.1[理学—数学]