Equations in wreath products
Group Theory
2024-10-08 v1 Formal Languages and Automata Theory
Logic
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.
Keywords
Cite
@article{arxiv.2410.04905,
title = {Equations in wreath products},
author = {Laurent Bartholdi and Ruiwen Dong and Leon Pernak and Jan Philipp Wächter},
journal= {arXiv preprint arXiv:2410.04905},
year = {2024}
}