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arXiv · 1002.2658

Two Remarks on First-Order Theories of Baumslag-Solitar Groups

Montserrat Casals-Ruiz·Ilya Kazachkov
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Abstract

In this note we characterise all finitely generated groups elementarily equivalent to a solvable Baumslag-Solitar group BS$(1,n)$. It turns out that a finitely generated group $G$ is elementarily equivalent to BS$(1,n)$ if and only if $G$ is isomorphic to BS$(1,n)$. Furthermore, we show that two Baumslag-Solitar groups are existentially (universally) equivalent if and only if they are elementarily equivalent if and only if they are isomorphic.

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Montserrat Casals-Ruiz, Ilya Kazachkov. 2010-02-12. Two Remarks on First-Order Theories of Baumslag-Solitar Groups. https://arxiv.org/abs/1002.2658

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