一类有限Abel群G的构造  

STRUCTURE OF A CLASS OF FINITE ABELIAN GROUPS G

作　　者：黄本文[1] 

机构地区：[1]武汉大学数学系

出　　处：《武汉大学学报（自然科学版）》1994年第3期21-28,共8页Journal of Wuhan University(Natural Science Edition)

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.

关 键 词：自同构 群构造 阿贝尔群 欧拉函数 

分 类 号：O152.1[理学—数学]