@Article{CMR-32-167, author = {Tao and Xu and and 18510 and and Tao Xu and Heguo and Liu and and 18511 and and Heguo Liu}, title = {Finitely Generated Torsion-Free Nilpotent Groups Admitting an Automorphism of Prime Order}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {32}, number = {2}, pages = {167--172}, 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 $2$.

}, 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} }