On groups whose geodesic growth is polynomial
Group Theory
2012-05-16 v3
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 has an element whose normal closure is abelian and of finite index, then has a finite generating set with respect to which the geodesic growth is polynomial (this includes all virtually cyclic groups).
Cite
@article{arxiv.1009.5051,
title = {On groups whose geodesic growth is polynomial},
author = {Martin Bridson and Jose Burillo and Murray Elder and Zoran Sunic},
journal= {arXiv preprint arXiv:1009.5051},
year = {2012}
}
Comments
11 pages, 1 figure