| 剩余有限Minimax可解群的4阶正则自同构 |
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| 引用本文： | 徐涛,刘合国.剩余有限Minimax可解群的4阶正则自同构[J].数学年刊A辑(中文版),2019(1):105-112. |
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| 作者姓名： | 徐涛 刘合国 |
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| 作者单位： | 河北工程大学数理学院, 邯郸 056038.,湖北大学数学与统计学院, 武汉 430062. |
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| 基金项目： | 本文受到国家自然科学基金(No.11771129,No.11626078),河北省高等学校青年拔尖人才计划项目,
湖北省高等学校优秀中青年科技创新团队计划(No.T201601),湖北省新世纪高层次人才工程专项基金和邯郸市科学技术研究与发展计划项目
(No.1723208068-5)的资助. |
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| 摘 要： | 设G是剩余有限minimax可解群,α是G的4阶正则自同构,则下面结果成立:(1)如果映射φ:G→G (g→g,α])是满射,那么G是中心子群被亚Abel群的扩张.(2)C_G(α~2)和G,n-1α~2]/G,nα~2](n∈Z~+)都是Abel群的有限扩张.
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| 关 键 词： | Residually finite minimax soluble group Regular automorphism Almost regular automorphism |
| 收稿时间： | 2015/10/7 0:00:00 |
| 修稿时间： | 2017/2/25 0:00:00 |
On Regular Automorphisms of Order Four of[2mm] Residually Finite Minimax Soluble Groups |
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| XU Tao and LIU Heguo.On Regular Automorphisms of Order Four of[2mm] Residually Finite Minimax Soluble Groups[J].Chinese Annals of Mathematics,2019(1):105-112. |
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| Authors: | XU Tao and LIU Heguo |
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| Institution: | Department of Science, Hebei University of Engineering,Handan 056038, China. and College of Mathematics and Statistics, Hubei University, Wuhan430062, China. |
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| Abstract: | Let $G$ be a residually finite minimax soluble group, and let $\alpha$ be a regular automorphism of order
four of $G$. Then
(1) If the map $\varphi:G\longrightarrow G$ defined by $g^{\varphi}=g,\alpha]$
is surjective, then $G$ is centre-by-metabelian.
(2) \ Both $C_{G}(\alpha^{2})$ and $G,~_{n-1}\alpha^{2}]/G,~_{n}\alpha^{2}]$ (where $n\in
\mathbb{Z}^{+}$) are abelian-by-finite. |
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| Keywords: | Residually finite minimax soluble group Regular automorphism Almost regular automorphism |
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