| 有限秩的可解群的正则自同构 |
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| 引用本文： | 徐涛,刘合国.有限秩的可解群的正则自同构[J].数学年刊A辑(中文版),2014,35(5):543-550. |
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| 作者姓名： | 徐涛 刘合国 |
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| 作者单位： | 河北工程大学理学院, 河北 邯郸 056038.;湖北大学数学系, 武汉 430062 |
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| 基金项目： | 国家自然科学基金(No.11371124), 湖北省高层次人才工程基金(No.070-016533)和河北工程大学博士专项基金(No.20120066) |
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| 摘 要： | 设G是有限秩的剩余有限可解群或是有限秩的剩余有限可解群的有限扩张,α是G的一个索数p阶正则自同构且φ:G→G(g→g,α])是满射,则G是幂零类不超过h(p)的幂零群,其中h(p)是只与p有关的函数.
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| 关 键 词： | 有限秩 剩余有限性 正则自同构 |
On Regular Automorphisms of Soluble Groups of Finite Rank |
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| XU Tao and LIU Heguo.On Regular Automorphisms of Soluble Groups of Finite Rank[J].Chinese Annals of Mathematics,2014,35(5):543-550. |
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| Authors: | XU Tao and LIU Heguo |
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| Institution: | School of Science, Hebei University of Engineering,
Handan 056038, Hebei, China.;Department of Mathematics, Hubei University,
Wuhan 430062, China. |
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| Abstract: | Let $G$ be either a
residually finite soluble group of finite rank or a finite extension
of a residually finite soluble group of finite rank. If $G$ has a regular
automorphism $\alpha$ of prime order $p$ and the map
$\varphi:~G\rightarrow G~~(g\mapsto g,\alpha])$ is
surjective, then $G$ is a nilpotent group of nilpotent class at most $h(p)$, where
$h(p)$ is a function depending only on $p$. |
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| Keywords: | Finite rank Residually finite Regular automorphism |
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