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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. COMBGRAF - Combinatòria, Teoria de Grafs i Aplicacions
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
Àrees temàtiques de la UPC::Matemàtiques i estadística
Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra
Geodesics (Mathematics)
Geodesic growth
virtually nilpotent group
virtually cyclic abelianization
Geodèsiques (Matemàtica)
Attribution-NonCommercial-NoDerivs 3.0 Spain

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