|A（G）|=2⁵p²（p为奇素数）的有限Abel群G

|A（G）|=2 5 p 2 （p为奇素数）的有限Abel群G Finite Abelian Groups with an Automurphism Group of Order 2 5 p 2 王秀花 WANG Xiuhua1 1 first-author 黄本文 HUANG Benwen2 2 孝感学院数学系 孝感学院数学系 Department of Mathematics, Xiaogan University Department of Mathematics, Xiaogan University 武汉大学数学与统计学院 武汉大学数学与统计学院 School of Mathematics and Statistics, Wuhan University School of Mathematics and Statistics, Wuhan University 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 25p2 （p is an odd and prime number）. For p=3,5, 17, G has 38, 19, 3 types respectively, while for p≠3,5,17, G has at most 34 types. 自同构群 Abel群 群构造 Euler函数 automorphism group abelian group structer of group Euler fuction O152.5 湖北省教育厅中青年人才项目（Q200726003）;孝感学院科研项目基金资助项目（z2008005） 2008-01-01 2021-04-01 1