摘要:
设
Cpβi 是
pβi 阶的循环群,其中p 为素数,1
≤i
≤4 。J. N. S. Bidwell利用矩阵表示方法得到了没有共同直因子的直积
Cpm× Cpn和
Cpβ1× Cpβ2× Cpβ3 的自同构群。本文采用同样的方法得到了直积
Cpβ1× Cpβ2× Cpβ3×Cpβ4 的自同构群的生成元和生成关系。
Let Cpβi be the cyclic group of order pβi where p is a prime number, and 1≤i≤4 . Using matrix representation, J. N. S. Bidwell got the automorphisms of direct products Cpm× Cpn , and Cpβ1× Cpβ2× Cpβ3 which have no common direct factor. In this paper, the generators of the automorphism of direct product Cpβ1× Cpβ2× Cpβ3×Cpβ4 and the relations between them are obtained.