Illinois Journal of Mathematics

On conjugacy separability of some Coxeter groups and parabolic-preserving automorphisms

Pierre-Emmanuel Caprace and Ashot Minasyan

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We prove that even Coxeter groups, whose Coxeter diagrams contain no $(4,4,2)$ triangles, are conjugacy separable. In particular, this applies to all right-angled Coxeter groups or word hyperbolic even Coxeter groups. For an arbitrary Coxeter group $W$, we also study the relationship between Coxeter generating sets that give rise to the same collection of parabolic subgroups. As an application, we show that if an automorphism of $W$ preserves the conjugacy class of every sufficiently short element then it is inner. We then derive consequences for the outer automorphism groups of Coxeter groups.

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Illinois J. Math., Volume 57, Number 2 (2013), 499-523.

First available in Project Euclid: 19 August 2014

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Primary: 20F55: Reflection and Coxeter groups [See also 22E40, 51F15] 20E26: Residual properties and generalizations; residually finite groups 20E36: Automorphisms of infinite groups [For automorphisms of finite groups, see 20D45]


Caprace, Pierre-Emmanuel; Minasyan, Ashot. On conjugacy separability of some Coxeter groups and parabolic-preserving automorphisms. Illinois J. Math. 57 (2013), no. 2, 499--523. doi:10.1215/ijm/1408453592.

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