｜A(G)｜=2^5P^2(p为奇素数)的有限Abel群G

Finite Abelian Groups with an Automurphism Group of Order 2~5p^2

利用有限Abel群G的自同构群A(G)的阶来讨论群G的构造,根据有限交换群的性质,推导出了|A(G)|=25p2(p为奇素数)的有限Abel群G的全部类型.当p=3时,G有38型;当p=5时,G有19型;当p=17时,G有3型;当p≠3,5,17时,G最多有34型.

This paper discusses the structures of finite abelian group G by oder of automorphism group A （G）. According to the characters of finite abelian group, we have obtained all types of finite abelian group G with the order of A（G） equals 2^5p^2（p is an odd and prime number）. For p=3,5, 17, Ghas 38, 19, 3 types respectively, while for p≠3,5,17, G has at most 34 types.