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On groups whose geodesic growth is polynomial

Author
Bridson, M.; Burillo, J.; Elder, M.; Šunic, Z.
Type of activity
Journal article
Journal
International journal of algebra and computation
Date of publication
2012-08
Volume
22
Number
5
First page
1
Last page
11
DOI
https://doi.org/10.1142/S0218196712500488 Open in new window
Repository
http://hdl.handle.net/2117/17183 Open in new window
URL
http://arxiv.org/pdf/1009.5051v3.pdf Open in new window
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)
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.
Keywords
Geodesic growth, virtually cyclic abelianization, virtually nilpotent group
Group of research
GAPCOMB - Geometric, Algebraic and Probabilistic Combinatorics

Participants

  • Bridson, Martin R.  (author)
  • Burillo Puig, Jose  (author)
  • Elder, Murray  (author)
  • Šunic, Z.  (author)