2024/07/01 by Gianluca Paolini, Paolini, Gianluca, Rizos Sklinos +1
Materials Science · Mathematics · #03C60 #20F55 #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Group Theory (math.GR) #Logic (math.LO) #Supramolecular Self-Assembly in Materials
paper · pdf · doi:10.48550/arxiv.2407.01141
openalex publication_date 2024/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.