A virtually 2-step nilpotent group with polynomial geodesic growth

Institute of Applied Mathematics And Mechanics of the National Academy of Sciences of Ukraine
Publication Type:
Journal Article
Algebra and Discrete Mathematics, 2022, 33, (2), pp. 21-21
Issue Date:
Full metadata record
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 nilpotent group having polynomial geodesic growth with respect to a certain finite generating set.
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