Highly Influenced

15 Excerpts

- Published 2012 in IJAC

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).

@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}
}