Finitely Generated Torsion-free Nilp otent Groups Admitting an Automorphism of Prime Order |
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| Authors: | Tao Xu & Heguo Liu |
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| Institution: | 1. Department of Science, Hebei University of Engineering, Handan, Hebei, 056038;2. Department of Mathematics, Hubei University, Wuhan, 430062 |
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| Abstract: | Let $G$ be a finitely generated torsion-free nilpotent group and $α$ an automorphism of prime order $p$ of $G$. If the map $φ : G→G$ defined by $g^φ = g, α]$ is surjective, then the nilpotent class of $G$ is at most $h(p)$, where $h(p)$ is a function
depending only on $p$. In particular, if $α^3 = 1$, then the nilpotent class of $G$ is at most $2$. |
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| Keywords: | torsion-free nilpotent group regular automorphism surjectivity |
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