Alex Bishop, Murray Elder
Published 2020-07-14Version 1
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.
Comments: 7 pages, 1 figure
On groups whose geodesic growth is polynomial
Finite generating sets of relatively hyperbolic groups and applications to geodesic languages
A new proof of Gromov's theorem on groups of polynomial growth
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