Bulletin of the Belgian Mathematical Society - Simon Stevin

On the Cayley graph of a generic finitely presented group

G. N. Arzhantseva and P.-A. Cherix

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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

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1102689123

Digital Object Identifier
doi:10.36045/bbms/1102689123

Mathematical Reviews number (MathSciNet)
MR2115727

Zentralblatt MATH identifier
1069.05038

Subjects
Primary: 05C25: Graphs and abstract algebra (groups, rings, fields, etc.) [See also 20F65] 20F06: Cancellation theory; application of van Kampen diagrams [See also 57M05] 20P05: Probabilistic methods in group theory [See also 60Bxx]

Keywords
Cayley graph small cancellation groups generic properties of groups

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


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