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Preprint Number 2660
2660. Gianluca Paolini and Rizos Sklinos Profinite rigidity of affine Coxeter groups E-mail: Submission date: 1 July 2024 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. Mathematics Subject Classification: 03C60, 20F55 Keywords and phrases: |
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