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arXiv · 2506.15494

Profinite rigidity of crystallographic groups arising from Lie theory

Davide Carolillo·Gianluca Paolini
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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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Davide Carolillo, Gianluca Paolini. 2025-06-18. Profinite rigidity of crystallographic groups arising from Lie theory. https://arxiv.org/abs/2506.15494

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