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Peer-reviewedCC BYSemigroup Forum

Equations in wreath products

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

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.

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Cite

BibTeXRIS
BibTeX
@article{pernak2026equations,
  title = {{Equations in wreath products}},
  author = {Leon Pernak and Ruiwen Dong and Jan Philipp Wächter and Laurent Bartholdi},
  journal = {Semigroup Forum},
  year = {2026},
  month = nov,
  doi = {10.1007/s00233-025-10511-8},
  url = {https://hal.science/hal-05849736v1},
  note = {CC BY},
}
RIS
TY  - JOUR
TI  - Equations in wreath products
AU  - Leon Pernak
AU  - Ruiwen Dong
AU  - Jan Philipp Wächter
AU  - Laurent Bartholdi
PY  - 2026
DA  - 2026/11/03
JO  - Semigroup Forum
DO  - 10.1007/s00233-025-10511-8
UR  - https://hal.science/hal-05849736v1
AB  - 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.
SN  - 0037-1912
SN  - 1432-2137
ER  -