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2012 Finiteness of outer automorphism groups of random right-angled {A}rtin groups
Matthew B Day
Algebr. Geom. Topol. 12(3): 1553-1583 (2012). DOI: 10.2140/agt.2012.12.1553


We consider the outer automorphism group Out(AΓ) of the right-angled Artin group AΓ of a random graph Γ on n vertices in the Erdős–Rényi model. We show that the functions n1(log(n)+ log(log(n))) and 1n1(log(n)+ log(log(n))) bound the range of edge probability functions for which Out(AΓ) is finite: if the probability of an edge in Γ is strictly between these functions as n grows, then asymptotically Out(AΓ) is almost surely finite, and if the edge probability is strictly outside of both of these functions, then asymptotically Out(AΓ) is almost surely infinite. This sharpens a result of Ruth Charney and Michael Farber.


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Matthew B Day. "Finiteness of outer automorphism groups of random right-angled {A}rtin groups." Algebr. Geom. Topol. 12 (3) 1553 - 1583, 2012.


Received: 21 June 2011; Revised: 10 April 2012; Accepted: 25 April 2012; Published: 2012
First available in Project Euclid: 19 December 2017

zbMATH: 1246.05141
MathSciNet: MR2966695
Digital Object Identifier: 10.2140/agt.2012.12.1553

Primary: 05C80 , 20E36 , 20F28 , 20F69
Secondary: 20F05

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

Rights: Copyright © 2012 Mathematical Sciences Publishers


Vol.12 • No. 3 • 2012
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