Profinite rigidity of crystallographic groups arising from Lie theory
Group Theory
2025-06-19 v1 Logic
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.
Cite
@article{arxiv.2506.15494,
title = {Profinite rigidity of crystallographic groups arising from Lie theory},
author = {Davide Carolillo and Gianluca Paolini},
journal= {arXiv preprint arXiv:2506.15494},
year = {2025}
}
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41 pages