July 1, 2024Open Access

Profinite rigidity of affine Coxeter groups

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Abstract

We prove that the irreducible affine Coxeter groups are first-order rigid and deduce from this that they are profinitely rigid in the absolute sense. We then show that the first-order theory of any irreducible affine Coxeter group does not have a prime model. Finally, we prove that universal Coxeter groups of finite rank are homogeneous, and that the same applies to every hyperbolic (in the sense of Gromov) one-ended right-angled Coxeter group.

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Paolini et al. (Mon,) studied this question.

synapsesocial.com/papers/68e62291b6db6435875b4c25 https://doi.org/https://doi.org/10.48550/arxiv.2407.01141

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1Profinite rigidity of affine Coxeter groups2024
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3Higman–Thompson groups and profinite properties of right-angled Coxeter groups2026
4Profinite rigidity of crystallographic groups arising from Lie theory2025
5The strong hull property for affine irreducible Coxeter groups of rank 32025

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