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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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

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1408453592

Digital Object Identifier
doi:10.1215/ijm/1408453592

Mathematical Reviews number (MathSciNet)
MR3263043

Zentralblatt MATH identifier
1306.20043

Subjects
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]

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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