Commun. Math. Res., 32 (2016), pp. 167-172.
Published online: 2021-03
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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 $2$.
}, issn = {2707-8523}, doi = {https://doi.org/10.13447/j.1674-5647.2016.02.09}, url = {http://global-sci.org/intro/article_detail/cmr/18675.html} }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 $2$.