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November 2004 On the Cayley graph of a generic finitely presented group
G. N. Arzhantseva, P.-A. Cherix
Bull. Belg. Math. Soc. Simon Stevin 11(4): 589-601 (November 2004). DOI: 10.36045/bbms/1102689123

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.

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G. N. Arzhantseva. P.-A. Cherix. "On the Cayley graph of a generic finitely presented group." Bull. Belg. Math. Soc. Simon Stevin 11 (4) 589 - 601, November 2004. https://doi.org/10.36045/bbms/1102689123

Information

Published: November 2004
First available in Project Euclid: 10 December 2004

zbMATH: 1069.05038
MathSciNet: MR2115727
Digital Object Identifier: 10.36045/bbms/1102689123

Subjects:
Primary: 05C25, 20F06, 20P05

Rights: Copyright © 2004 The Belgian Mathematical Society

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Vol.11 • No. 4 • November 2004
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