The Profinite Rigidity of Free Metabelian Groups
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912461491273728 |
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| author | Wykowski, Julian |
| author_facet | Wykowski, Julian |
| contents | We prove that finitely generated free metabelian groups $Ψ_n$ are profinitely rigid in the absolute sense: they are distinguished by their finite quotients among all finitely generated residually finite groups. The proof is based on a previous result of the author governing profinite rigidity for modules over Noetherian domains, as well as a homological characterisation of free metabelian groups due to Groves--Miller. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_10321 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Profinite Rigidity of Free Metabelian Groups Wykowski, Julian Group Theory 20E18, 20F16 (Primary) 13D07, 13C10, 13C60 (Secondary) We prove that finitely generated free metabelian groups $Ψ_n$ are profinitely rigid in the absolute sense: they are distinguished by their finite quotients among all finitely generated residually finite groups. The proof is based on a previous result of the author governing profinite rigidity for modules over Noetherian domains, as well as a homological characterisation of free metabelian groups due to Groves--Miller. |
| title | The Profinite Rigidity of Free Metabelian Groups |
| topic | Group Theory 20E18, 20F16 (Primary) 13D07, 13C10, 13C60 (Secondary) |
| url | https://arxiv.org/abs/2503.10321 |