On groups whose geodesic growth is polynomial

Publication Type:
Journal Article
Citation:
International Journal of Algebra and Computation, 2012, 22 (5)
Issue Date:
2012-01-01
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© World Scientific Publishing Company. This paper 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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