Outer automorphism groups of right-angled Coxeter groups are either\n large or virtually abelian

2017/06/23 by Andrew W. Sale, Sale, Andrew, Tim Susse +1 · 1 citation
Computer Science · Mathematics · #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR) #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1706.07873

openalex publication_date 2017/06/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We generalise the notion of a separating intersection of links (SIL) to give\nnecessary and sufficient criteria on the defining graph \Γ of a\nright-angled Coxeter group W_\Γ so that its outer automorphism group is\nlarge: that is, it contains a finite index subgroup that admits the free group\nF₂ as a quotient. When Out(W_\Γ) is not large, we show it is virtually\nabelian. We also show that the same dichotomy holds for the outer automorphism\ngroups of graph products of finite abelian groups. As a consequence, these\ngroups have property (T) if and only if they are finite, or equivalently\n\Γ contains no SIL.\n

Cited by

• L²-torsion of automorphisms

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