Diophantine Problem in Some Metabelian Groups

2019/03/24 by Kharlampovich, Olga, Lopez, Laura, Miasnikov, Alexei · 3 citations
#20F70 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1903.10068

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 ℤ, where A is a finitely generated abelian group and ℤ is an infinite cyclic group, is decidable.

Cited by

• The Diophantine problem in the Baumslag-Gersten group
• Decidability of equations and first-order theory in Seifert 3-manifold groups
• One variable equations over the lamplighter group

Related

• Equations in wreath products
• Quadratic equations in metabelian Baumslag-Solitar groups
• Orientable quadratic equations in free metabelian groups
• Diophantine problems in solvable groups
• Spherical quadratic equations in free metabelian groups