| 一类有限Abel群G的构造 |
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| 引用本文： | 黄本文. 一类有限Abel群G的构造[J]. 武汉大学学报(理学版), 1994, 0(3) |
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| 作者姓名： | 黄本文 |
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| 作者单位： | 武汉大学数学系 |
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| 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．
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| 关 键 词： | Abel群，自同构，群构造，Euler函数 |
STRUCTURE OF A CLASS OF FINITE ABELIAN GROUPS G |
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| Huang Benwen. STRUCTURE OF A CLASS OF FINITE ABELIAN GROUPS G[J]. JOurnal of Wuhan University:Natural Science Edition, 1994, 0(3) |
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| Authors: | Huang Benwen |
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| Abstract: | 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. |
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| Keywords: | Abel group automorphism structure of group Euler function |
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