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math.GR2026
Homogeneity in Coxeter groups and split crystallographic groups
Simon André, Gianluca Paolini
We prove that affine Coxeter groups, even hyperbolic Coxeter groups and one-ended hyperbolic Coxeter groups are homogeneous in the sense of model theory. More generally, we prove t…
math.GR2025
Profinite rigidity of crystallographic groups arising from Lie theory
Davide Carolillo, Gianluca Paolini
We prove that every finite direct product of crystallographic groups arising from an irreducible root system (in the sense of Lie theory) is profinitely rigid (equiv. first-order r…
math.GR2024
Profinite rigidity of affine Coxeter groups
Gianluca Paolini, Rizos Sklinos
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-or…