Geodesic
Finiteness of outer automorphism groups of random right-angled Artin groups
Day, Matthew B1
1Department of Mathematical Sciences, SCEN 301, University of Arkansas, Fayetteville, AR 72701, USA
Algebraic and Geometric Topology, Tome 12 (2012) no. 3, pp. 1553-1583
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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 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(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.

DOI : 10.2140/agt.2012.12.1553
Classification : 05C80, 20E36, 20F28, 20F69, 20F05
Keywords: right-angled Artin group, random graph, automorphism group of group

Day, Matthew B  1

1 Department of Mathematical Sciences, SCEN 301, University of Arkansas, Fayetteville, AR 72701, USA 
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Day, Matthew B. Finiteness of outer automorphism groups of random right-angled Artin groups. Algebraic and Geometric Topology, Tome 12 (2012) no. 3, pp. 1553-1583. doi: 10.2140/agt.2012.12.1553

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