Quadratic equations in metabelian Baumslag-Solitar groups
| Autor: | Mandel, Richard, Ushakov, Alexander |
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| Rok vydání: | 2023 |
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| Druh dokumentu: | Working Paper |
| Popis: | For a finitely generated group $G$, the \emph{Diophantine problem} over $G$ is the algorithmic problem of deciding whether a given equation $W(z_1,z_2,\ldots,z_k) = 1$ (perhaps restricted to a fixed subclass of equations) has a solution in $G$. In this paper, we investigate the algorithmic complexity of the Diophantine problem for the class $\mathcal{C}$ of quadratic equations over the metabelian Baumslag-Solitar groups $\mathbf{BS}(1,n)$. We prove that this problem is $\mathbf{NP}$-complete whenever $n\neq \pm 1$, and determine the algorithmic complexity for various subclasses (orientable, nonorientable etc.) of $\mathcal{C}$. Comment: 19 pages |
| Databáze: | arXiv |
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