## Illinois Journal of Mathematics

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

#### Abstract

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.

#### Article information

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

Dates
First available in Project Euclid: 19 August 2014

https://projecteuclid.org/euclid.ijm/1408453592

Digital Object Identifier
doi:10.1215/ijm/1408453592

Mathematical Reviews number (MathSciNet)
MR3263043

Zentralblatt MATH identifier
1306.20043

#### Citation

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. https://projecteuclid.org/euclid.ijm/1408453592

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