Diophantine Problem in Some Metabelian Groups

Abstract

In this paper we show that Diophantine problem for quadratic equations in Baumslag-Solitar groups $BS(1,k)$ and in wreath products $A\wr \mathbb{Z}$, where $A$ is a finitely generated abelian group and $\mathbb{Z}$ is an infinite cyclic group, is decidable.

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