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2012 Random groups arising as graph products
Ruth Charney, Michael Farber
Algebr. Geom. Topol. 12(2): 979-995 (2012). DOI: 10.2140/agt.2012.12.979


In this paper we study the hyperbolicity properties of a class of random groups arising as graph products associated to random graphs. Recall, that the construction of a graph product is a generalization of the constructions of right-angled Artin and Coxeter groups. We adopt the Erdös and Rényi model of a random graph and find precise threshold functions for hyperbolicity (or relative hyperbolicity). We also study automorphism groups of right-angled Artin groups associated to random graphs. We show that with probability tending to one as n, random right-angled Artin groups have finite outer automorphism groups, assuming that the probability parameter p is constant and satisfies 0.2929<p<1.


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Ruth Charney. Michael Farber. "Random groups arising as graph products." Algebr. Geom. Topol. 12 (2) 979 - 995, 2012.


Received: 1 February 2011; Accepted: 3 December 2011; Published: 2012
First available in Project Euclid: 19 December 2017

zbMATH: 1280.20046
MathSciNet: MR2928902
Digital Object Identifier: 10.2140/agt.2012.12.979

Primary: 20P05
Secondary: 20F36 , 57M07

Keywords: automorphisms of Artin groups , hyperbolic group , random group , right angled Artin group

Rights: Copyright © 2012 Mathematical Sciences Publishers


Vol.12 • No. 2 • 2012
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