June 30, 2024Open Access

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

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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 Z, and describe in algebraic terms all groups that are elementarily equivalent to BS (1, k).

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Daniyarova et al. (Sun,) studied this question.

synapsesocial.com/papers/68e6278eb6db6435875b9d7c https://doi.org/https://doi.org/10.48550/arxiv.2407.00642

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