Abstract
We consider the outer automorphism group of the right-angled Artin group of a random graph on vertices in the Erdős–Rényi model. We show that the functions and bound the range of edge probability functions for which is finite: if the probability of an edge in is strictly between these functions as grows, then asymptotically is almost surely finite, and if the edge probability is strictly outside of both of these functions, then asymptotically is almost surely infinite. This sharpens a result of Ruth Charney and Michael Farber.
Citation
Matthew B Day. "Finiteness of outer automorphism groups of random right-angled {A}rtin groups." Algebr. Geom. Topol. 12 (3) 1553 - 1583, 2012. https://doi.org/10.2140/agt.2012.12.1553
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