TY - JOUR T1 - Finitely Generated Torsion-Free Nilpotent Groups Admitting an Automorphism of Prime Order AU - Xu , Tao AU - Liu , Heguo JO - Communications in Mathematical Research VL - 2 SP - 167 EP - 172 PY - 2021 DA - 2021/03 SN - 32 DO - http://doi.org/10.13447/j.1674-5647.2016.02.09 UR - https://global-sci.org/intro/article_detail/cmr/18675.html KW - torsion-free nilpotent group, regular automorphism, surjectivity. AB -
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 $2$.