On groups whose geodesic growth is polynomial

Details On groups whose geodesic growth is polynomial On groups whose geodesic growth is polynomial

2010-09-26

arxiv.org/abs/1009.5051v3

Mathematics

Group Theory

11 pages, 1 figure

Scientific paper

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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