Profinite rigidity of affine Coxeter groups
Group Theory
2024-07-03 v2 Logic
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.
Cite
@article{arxiv.2407.01141,
title = {Profinite rigidity of affine Coxeter groups},
author = {Gianluca Paolini and Rizos Sklinos},
journal= {arXiv preprint arXiv:2407.01141},
year = {2024}
}