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arXiv · 1103.0479

Finiteness of outer automorphism groups of random right-angled Artin groups

Matthew B. Day
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Abstract

We consider the outer automorphism group Out(A_Gamma) of the right-angled Artin group A_Gamma of a random graph Gamma on n vertices in the Erdos--Renyi model. We show that the functions (log(n)+log(log(n)))/n and 1-(log(n)+log(log(n)))/n bound the range of edge probability functions for which Out(A_Gamma) is finite: if the probability of an edge in Gamma is strictly between these functions as n grows, then asymptotically Out(A_Gamma) is almost surely finite, and if the edge probability is strictly outside of both of these functions, then asymptotically Out(A_Gamma) is almost surely infinite. This sharpens results of Ruth Charney and Michael Farber from their preprint "Random groups arising as graph products", arXiv:1006.3378v1.

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Matthew B. Day. 2011-06-14. Finiteness of outer automorphism groups of random right-angled Artin groups. https://doi.org/10.2140/agt.2012.12.1553

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