Profinite rigidity of crystallographic groups arising from Lie theory
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866916799448088576 |
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| author | Carolillo, Davide Paolini, Gianluca |
| author_facet | Carolillo, Davide Paolini, Gianluca |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_15494 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Profinite rigidity of crystallographic groups arising from Lie theory Carolillo, Davide Paolini, Gianluca Group Theory Logic 03C60, 20F55, 20E18, 20H15 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. |
| title | Profinite rigidity of crystallographic groups arising from Lie theory |
| topic | Group Theory Logic 03C60, 20F55, 20E18, 20H15 |
| url | https://arxiv.org/abs/2506.15494 |