On the Cayley graph of a generic finitely presented group
G. N. Arzhantseva and P.-A. Cherix
Source: Bull. Belg. Math. Soc. Simon Stevin Volume 11, Number 4 (2004), 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.
Primary Subjects: 05C25, 20F06, 20P05
Keywords: Cayley graph; small cancellation groups; generic properties of groups
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Bulletin of the Belgian Mathematical Society - Simon Stevin
