On groups whose geodesic growth is polynomial

Bridson, Martin R.; Burillo Puig, José; Elder, Murray; Šunic, Z.

doi:10.1142/S0218196712500488

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Document typeArticle

Defense date2012-08

Rights accessRestricted access - publisher's policy

Except where otherwise noted, content on this work is licensed under a Creative Commons license : Attribution-NonCommercial-NoDerivs 3.0 Spain

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 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.

URIhttp://hdl.handle.net/2117/17183

DOI10.1142/S0218196712500488

ISSN0218-1967

Publisher versionhttp://arxiv.org/pdf/1009.5051v3.pdf

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