A virtually 2-step nilpotent group with polynomial geodesic growth

• Date: 2022
• Main Authors: Bishop, A., Elder, M.
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2022
• Subjects: geodesic growth; discrete Heisenberg group; 20F65; 20F18; 20F69
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1667
• Journal Title: Algebra and Discrete Mathematics

A direct consequence of Gromov's theorem is that if a group has polynomial geodesic growth with respect to some finite generating set then it is virtually nilpotent. However, until now the only examples known were virtually abelian. In this note we furnish an example of a virtually 2-step nilpo...