一类有限Abel群G的构造

一类有限Abel群G的构造 STRUCTURE OF A CLASS OF FINITE ABELIAN GROUPS G 黄本文 Huang Benwen 1 first-author 武汉大学数学系 武汉大学数学系 Department of Mathematics, Wuhan University Department of Mathematics, Wuhan University 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. Abel群 自同构 群构造 Euler函数 Abel group Automorphism Structure of group Euler function O152.1 1994-03-01 2021-04-01 3