On conjugacy separability of some Coxeter groups and parabolic-preserving automorphisms
On conjugacy separability of some Coxeter groups and parabolic-preserving automorphisms
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.
499-523
Caprace, Pierre-Emmanuel
b07cf9c5-07b8-4b19-9508-f0f4da9d7577
Minasyan, Ashot
3de640f5-d07b-461f-b130-5b1270bfdb3d
August 2014
Caprace, Pierre-Emmanuel
b07cf9c5-07b8-4b19-9508-f0f4da9d7577
Minasyan, Ashot
3de640f5-d07b-461f-b130-5b1270bfdb3d
Caprace, Pierre-Emmanuel and Minasyan, Ashot
(2014)
On conjugacy separability of some Coxeter groups and parabolic-preserving automorphisms.
Illinois Journal of Mathematics, 57 (2), .
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.
Text
EvenCox_revised-2.pdf
- Accepted Manuscript
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Accepted/In Press date: 9 April 2013
Published date: August 2014
Organisations:
Pure Mathematics
Identifiers
Local EPrints ID: 356146
URI: http://eprints.soton.ac.uk/id/eprint/356146
ISSN: 0019-2082
PURE UUID: ee30d065-ea90-4b80-b962-c8b8a56f0ab0
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Date deposited: 11 Sep 2013 10:36
Last modified: 15 Mar 2024 03:29
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Author:
Pierre-Emmanuel Caprace
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