On the number of outer automorphisms of the automorphism group of a right-angled Artin group

2013/06/27 by Neil J. Fullarton, Fullarton, Neil J.
Mathematics · #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR) #math.GR #math.GT

paper · pdf · doi:10.48550/arxiv.1306.6549

openalex publication_date 2013/06/27 · arxiv created 2015/10/05 · arxiv updated 2015/10/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that there is no uniform upper bound on |Out(Aut(A))| when A ranges over all right-angled Artin groups. This is in contrast with the cases where A is free or free abelian: for all n, Dyer-Formanek and Bridson-Vogtmann showed that Out(Aut(F_n)) = 1, while Hua-Reiner showed |Out(Aut(Zⁿ)| = |Out(GL(n,Z))| < 5. We also prove the analogous theorem for Out(Out(A)). We establish our results by giving explicit examples; one useful tool is a new class of graphs called austere graphs.

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