| 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,2014,35(5):543~550 |
| 有限秩的可解群的正则自同构 |
| On Regular Automorphisms of Soluble Groups of Finite Rank |
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| DOI： |
| 中文关键词: 有限秩, 剩余有限性, 正则自同构 |
| 英文关键词:Finite rank, Residually finite, Regular automorphism |
| 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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| 中文摘要: |
| 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,
$\alpha$是$G$的一个素数$p$阶正则自同构且$\varphi: ~G\rightarrow
G~~(g\mapsto [g,\alpha])$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. |
| 英文摘要: |
| 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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