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arXiv · 2407.01141

Profinite rigidity of affine Coxeter groups

Gianluca Paolini·Rizos Sklinos
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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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Gianluca Paolini, Rizos Sklinos. 2024-07-02. Profinite rigidity of affine Coxeter groups. https://arxiv.org/abs/2407.01141

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