Groups elementarily equivalent to metabelian Baumslag$-$Solitar groups and regular bi-interpretability

Evelina Daniyarova; Alexei Myasnikov

doi:10.1016/j.apal.2025.103695

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arXiv · 2407.00642

Groups elementarily equivalent to metabelian Baumslag$-$Solitar groups and regular bi-interpretability

Evelina Daniyarova·Alexei Myasnikov

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Abstract

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 $BS(1,k)$.

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Evelina Daniyarova, Alexei Myasnikov. 2024-06-30. Groups elementarily equivalent to metabelian Baumslag$-$Solitar groups and regular bi-interpretability. https://doi.org/10.1016/j.apal.2025.103695

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