## Bulletin of the Belgian Mathematical Society - Simon Stevin

### On the Cayley graph of a generic finitely presented group

#### 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.

#### Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 11, Number 4 (2004), 589-601.

Dates
First available in Project Euclid: 10 December 2004

https://projecteuclid.org/euclid.bbms/1102689123

Digital Object Identifier
doi:10.36045/bbms/1102689123

Mathematical Reviews number (MathSciNet)
MR2115727

Zentralblatt MATH identifier
1069.05038

#### Citation

Arzhantseva, G. N.; Cherix, P.-A. On the Cayley graph of a generic finitely presented group. Bull. Belg. Math. Soc. Simon Stevin 11 (2004), no. 4, 589--601. doi:10.36045/bbms/1102689123. https://projecteuclid.org/euclid.bbms/1102689123