On groups whose geodesic growth is polynomial
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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)
CitationBridson, M. [et al.]. On groups whose geodesic growth is polynomial. "International journal of algebra and computation", Agost 2012, vol. 22, núm. 5, p. 1-11.
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