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<p>We survey solvability of equations in wreath products of groups, and prove that the quadratic diophantine problem is solvable in wreath products of Abelian groups. We consider the related question of determining commutator width, and prove that the quadratic diophantine problem is also solvable in Baumslag’s finitely presented metabelian group. This text is a short version of an extensive article by the first-named authors.</p>

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Equations in wreath products

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年3月21日

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  • Leon Pernak,
  • Ruiwen Dong,
  • Jan Philipp Wächter,
  • Laurent Bartholdi

摘要

We survey solvability of equations in wreath products of groups, and prove that the quadratic diophantine problem is solvable in wreath products of Abelian groups. We consider the related question of determining commutator width, and prove that the quadratic diophantine problem is also solvable in Baumslag’s finitely presented metabelian group. This text is a short version of an extensive article by the first-named authors.