Groups elementarily equivalent to metabelian Baumslag$-$Solitar groups and regular bi-interpretability
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916307638681600 |
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| author | Daniyarova, Evelina Myasnikov, Alexei |
| author_facet | Daniyarova, Evelina Myasnikov, Alexei |
| contents | We prove that metabelian Baumslag$-$Solitar group $BS(1,k)$, $k>1$, is (strongly) regularly bi-interpretable with the ring of integers $\mathbb{Z}$, and describe in algebraic terms all groups that are elementarily equivalent to $BS(1,k)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_00642 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Groups elementarily equivalent to metabelian Baumslag$-$Solitar groups and regular bi-interpretability Daniyarova, Evelina Myasnikov, Alexei Group Theory Logic We prove that metabelian Baumslag$-$Solitar group $BS(1,k)$, $k>1$, is (strongly) regularly bi-interpretable with the ring of integers $\mathbb{Z}$, and describe in algebraic terms all groups that are elementarily equivalent to $BS(1,k)$. |
| title | Groups elementarily equivalent to metabelian Baumslag$-$Solitar groups and regular bi-interpretability |
| topic | Group Theory Logic |
| url | https://arxiv.org/abs/2407.00642 |