Algebraic & Geometric Topology 12 (2012) 1553–1583

DOI: 10.2140/agt.2012.12.1553

Abstract

We consider the outer automorphism group Out(A_Γ) of the right-angled Artin group A_Γ of a random graph Γ on n vertices in the Erdős–Rényi model. We show that the functions n⁻¹(log(n) + log(log(n))) and 1 −n⁻¹(log(n) + log(log(n))) bound the range of edge probability functions for which Out(A_Γ) is finite: if the probability of an edge in Γ is strictly between these functions as n grows, then asymptotically Out(A_Γ) is almost surely finite, and if the edge probability is strictly outside of both of these functions, then asymptotically Out(A_Γ) is almost surely infinite. This sharpens a result of Ruth Charney and Michael Farber.

Keywords

right-angled Artin group, random graph, automorphism group of group

Mathematical Subject Classification

Primary: 05C80, 20E36, 20F28, 20F69

Secondary: 20F05

References

Publication

Received: 21 June 2011
Revised: 10 April 2012
Accepted: 25 April 2012
Published: 15 July 2012

Authors