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On the Cayley graph of a generic finitely presented group

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Published in Bulletin of the Belgian Mathematical Society - Simon Stevin. 2004, vol. 11, no. 4, p. 589-601
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 graphSmall cancellation groupsGeneric properties of groups
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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. https://archive-ouverte.unige.ch/unige:12272

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Deposited on : 2010-11-01

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