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On groups whose geodesic growth is polynomial

Autor
Bridson, M.; Burillo, J.; Elder, M.; Šunic, Z.
Tipus d'activitat
Article en revista
Revista
International journal of algebra and computation
Data de publicació
2012-08
Volum
22
Número
5
Pàgina inicial
1
Pàgina final
11
DOI
https://doi.org/10.1142/S0218196712500488 Obrir en finestra nova
Repositori
http://hdl.handle.net/2117/17183 Obrir en finestra nova
URL
http://arxiv.org/pdf/1009.5051v3.pdf Obrir en finestra nova
Resum
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)
Citació
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.
Paraules clau
Geodesic growth, virtually cyclic abelianization, virtually nilpotent group
Grup de recerca
GAPCOMB - Geometric, Algebraic and Probabilistic Combinatorics

Participants

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