Two Remarks on First-Order Theories of Baumslag-Solitar Groups
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 tw...
| Main Authors: | , |
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| Format: | Journal article |
| Language: | English |
| Published: |
2010
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| Summary: | 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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