摘要
确定有限阶群的构造，是有限群理论的核心问题，本文从群Ｇ的自同构群间（Ｇ）入手，利用群Ｇ的自同构群Ａ（Ｇ）的阶来刻划群Ｇ的构造，采用了一种较为简便的方法证明了下面的结果：定理设Ｇ是有限Ａｂｅｌ群，若｜Ａ（Ｇ）｜＝２７ｐ（ｐ为奇素数），于是１）当ｐ＝３时，Ｇ有４３型，２）当ｐ＝５时，Ｇ有２９型；３）当ｐ＝１７时，Ｇ有１４型，４）当ｐ≠３，５，１７时，Ｇ最多有４５型．
In this paper we have discussed structures of Abelian group G by order | A(G)| of automorphism group and have obtained all types of finite Abelian group G When the order of A(G) equals 27p (p is odd prime). The following theorem is proved:Theorem Let G be finite Abelian group, if |A(G) |= 27p(p is odd prime),then 1) G has 43 types when p=3;2) G has 29 types when p= 5;3) G has 14 types when p=17;4) G has no more than 45 typed when p3,5, 17.
出处
《武汉大学学报（自然科学版）》
CSCD
1994年第3期21-28,共8页
Journal of Wuhan University(Natural Science Edition)
关键词
自同构
群构造
阿贝尔群
欧拉函数
Abel group, automorphism,structure of group, Euler function
