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Mathematics of Computation

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The Diophantine problem in some metabelian groups

Authors: Olga Kharlampovich, Laura López and Alexei Myasnikov
Journal: Math. Comp. 89 (2020), 2507-2519
MSC (2010): Primary 20F16, 20F70
Published electronically: April 16, 2020
MathSciNet review: 4109575
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Abstract: In this paper we show that the Diophantine problem in solvable 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, i.e., there is an algorithm that, given a finite system of equations with constants in such a group, decides whether or not the system has a solution in the group.

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Additional Information

Olga Kharlampovich
Affiliation: Department of Mathematics and Statistics, Hunter College and Graduate Center of City University of New York, Room 919/944 East, 695 Park Avenue, New York, New York 10065

Laura López
Affiliation: The Graduate Center, City University of New York, 365 Fifth Avenue, New York, New York 10016

Alexei Myasnikov
Affiliation: Department of Mathematical Sciences, Stevens Institute of Technology, One Castle Point Terrace, Hoboken, New Jersey 07030

Received by editor(s): July 28, 2019
Received by editor(s) in revised form: October 31, 2019, and January 11, 2020
Published electronically: April 16, 2020
Additional Notes: The first author gratefully acknowledges support over the years by grant 422503 from the Simons Foundation.
Article copyright: © Copyright 2020 American Mathematical Society