| 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,2019,(1):105~112 |
| 剩余有限Minimax可解群的4阶正则自同构 |
| On Regular Automorphisms of Order Four of[2mm] Residually Finite Minimax Soluble Groups |
| Received:October 07, 2015 Revised:February 25, 2017 |
| DOI：10.16205/j.cnki.cama.2019.0009 |
| 中文关键词: Residually finite, minimax soluble group, Regular automorphism, Almost regular automorphism |
| 英文关键词:Residually finite, minimax soluble group, Regular automorphism, Almost regular automorphism |
| 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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| 中文摘要: |
| 设$G$是剩余有限$\mbox{minimax}$可解群,
$\alpha$是$G$的4阶正则自同构, 则下面结果成立:
(1) 如果映射$\varphi: G\longrightarrow
G~(g\longmapsto [g,\alpha])$是满射,
那么$G$是中心子群被亚$\mbox{Abel}$群的扩张.
(2) $C_{G}(\alpha^{2})$和$[G,~_{n-1}\alpha^{2}]/[G,~_{n}\alpha^{2}]$($n\in
\mathbb{Z}^{+}$)~都是$\mbox{Abel}$群的有限扩张. |
| 英文摘要: |
| 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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