Volume 32, Issue 2
Finitely Generated Torsion-Free Nilpotent Groups Admitting an Automorphism of Prime Order

Commun. Math. Res., 32 (2016), pp. 167-172.

Published online: 2021-03

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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 $2$.

• Keywords

torsion-free nilpotent group, regular automorphism, surjectivity.

20E36

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@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} }
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 $2$.

Tao Xu & Heguo Liu. (2021). Finitely Generated Torsion-Free Nilpotent Groups Admitting an Automorphism of Prime Order. Communications in Mathematical Research . 32 (2). 167-172. doi:10.13447/j.1674-5647.2016.02.09
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