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Scientific article
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English

On the Cayley graph of a generic finitely presented group

Published inBulletin of the Belgian Mathematical Society Simon Stevin, vol. 11, no. 4, p. 589-601
Publication date2004
Abstract

We prove that in a certain statistical sense the Cayley graph of almost every finitely presented group with $m\ge 2$ generators contains a subdivision of the complete graph on $l\le 2m+1$ vertices. In particular, this Cayley graph is non planar. We also show that some group constructions preserve the planarity.

Keywords
  • Cayley graph
  • Small cancellation groups
  • Generic properties of groups
Citation (ISO format)
ARZHANTSEVA, Goulnara N., CHERIX, Pierre-Alain. On the Cayley graph of a generic finitely presented group. In: Bulletin of the Belgian Mathematical Society Simon Stevin, 2004, vol. 11, n° 4, p. 589–601.
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Article (Accepted version)
accessLevelPublic
Identifiers
  • PID : unige:12272
ISSN of the journal1370-1444
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