On groups whose geodesic growth is polynomial

Title: On groups whose geodesic growth is polynomial
Creator: Bridson, Martin R.; Burillo, José; Elder, Murray; Šunić, Zoran
Relation: International Journal of Algebra and Computation Vol. 22, Issue 5
Publisher Link: http://dx.doi.org/10.1142/S0218196712500488
Publisher: World Scientific Publishing
Resource Type: journal article
Date: 2012
Description: 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).
Subject: geodesic growth; virtually nilpotent group; virtually cyclic abelianization
Identifier: http://hdl.handle.net/1959.13/931710
Identifier: uon:11143
Identifier: ISSN:0218-1967
Rights: Electronic version of an article published as International Journal of Algebra and Computation, Volume 22, Issue 5, 2012, 1250048 [10.1142/S0218196712500488] © copyright World Scientific Publishing Company, http://www.worldscientific.com/worldscinet/ijac
Language: eng
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