On groups whose geodesic growth is polynomial

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dc.contributor	Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada IV
dc.contributor	Universitat Politècnica de Catalunya. COMBGRAPH - Combinatòria, Teoria de Grafs i Aplicacions
dc.contributor.author	Bridson, Martin R.
dc.contributor.author	Burillo Puig, José
dc.contributor.author	Elder, Murray
dc.contributor.author	Šunic, Z.
dc.date	2012-08
dc.identifier.citation	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.
dc.identifier.citation	0218-1967
dc.identifier.citation	10.1142/S0218196712500488
dc.identifier.uri	http://hdl.handle.net/2117/17183
dc.language.iso	eng
dc.relation	http://arxiv.org/pdf/1009.5051v3.pdf
dc.rights	Attribution-NonCommercial-NoDerivs 3.0 Spain
dc.rights	info:eu-repo/semantics/openAccess
dc.rights	http://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subject	Àrees temàtiques de la UPC::Matemàtiques i estadística
dc.subject	Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra
dc.subject	Geodesics (Mathematics)
dc.subject	Àlgebra
dc.subject	Geodesic growth
dc.subject	virtually nilpotent group
dc.subject	virtually cyclic abelianization
dc.subject	Geodèsiques (Matemàtica)
dc.subject	Algebra
dc.title	On groups whose geodesic growth is polynomial
dc.type	info:eu-repo/semantics/publishedVersion
dc.type	info:eu-repo/semantics/article
dc.description.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)
dc.description.abstract	Peer Reviewed

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