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Profinite rigidity of crystallographic groups arising from Lie theory
Published 18 Jun 2025 in math.GR and math.LO | (2506.15494v1)
Abstract: 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 rigid). This is a generalization of recent proofs of profinite rigidity of affine Coxeter groups [1, 7, 22]. Our proof uses model theory.
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