On Groups whose Geodesic Growth is Polynomial

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).

DOI: 10.1142/S0218196712500488

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Cite this paper

@article{Bridson2012OnGW, title={On Groups whose Geodesic Growth is Polynomial}, author={Martin R. Bridson and Jos{\'e} Burillo and Murray Elder and Zoran Sunic}, journal={IJAC}, year={2012}, volume={22} }