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arXiv · 1009.5051

On groups whose geodesic growth is polynomial

Martin Bridson·Jose Burillo·Murray Elder·Zoran Sunic
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Abstract

This note records some observations concerning geodesic growth functions. If a nilpotent group is not virtually cyclic then it has exponential geodesic growth with respect to all finite generating sets. On the other hand, if a finitely generated group $G$ has an element whose normal closure is abelian and of finite index, then $G$ has a finite generating set with respect to which the geodesic growth is polynomial (this includes all virtually cyclic groups).

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Martin Bridson, Jose Burillo, Murray Elder, Zoran Sunic. 2012-03-06. On groups whose geodesic growth is polynomial. https://doi.org/10.1142/s0218196712500488

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