Equations in wreath products
<|reference_start|>Equations in wreath products: 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.<|reference_end|>
@article{bartholdi2024equations,
    title={Equations in wreath products},
    author={Laurent Bartholdi, Ruiwen Dong, Leon Pernak, Jan Philipp W"achter},
    journal={arXiv preprint arXiv:2410.04905},
    year={2024},
    archivePrefix={arXiv},
    eprint={2410.04905},
    primaryClass={math.GR cs.FL math.LO}
}