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On groups whose geodesic growth is polynomial Bridson, Martin R. Burillo Puig, José Elder, Murray Šunic, Z. Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada IV Universitat Politècnica de Catalunya. COMBGRAPH - Combinatòria, Teoria de Grafs i Aplicacions Àrees temàtiques de la UPC::Matemàtiques i estadística Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra Geodesics (Mathematics) Àlgebra Geodesic growth virtually nilpotent group virtually cyclic abelianization Geodèsiques (Matemàtica) Algebra 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) Peer Reviewed Postprint (published version) 2012-08 Article Bridson, 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. 0218-1967 https://hdl.handle.net/2117/17183 10.1142/S0218196712500488 eng http://arxiv.org/pdf/1009.5051v3.pdf http://creativecommons.org/licenses/by-nc-nd/3.0/es/ Restricted access - publisher's policy Attribution-NonCommercial-NoDerivs 3.0 Spain 11 p. application/pdf