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

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

2010-02-12

arxiv.org/abs/1002.2658v2

Mathematics

Group Theory

5 pages, no figures

Scientific paper

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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