English

Quadratic equations in the lamplighter group

Group Theory 2024-12-05 v2

Abstract

In this paper we study the complexity of solving quadratic equations in the lamplighter group. We give a complete classification of cases (depending on genus and other characteristics of a given equation) when the problem is NP\mathbf{NP}-complete or polynomial-time decidable. We notice that the conjugacy problem can be solved in linear time. Finally, we prove that the problem belongs to the class XP\mathbf{XP}.

Keywords

Cite

@article{arxiv.2401.08589,
  title  = {Quadratic equations in the lamplighter group},
  author = {Alexander Ushakov and Chloe Weiers},
  journal= {arXiv preprint arXiv:2401.08589},
  year   = {2024}
}
R2 v1 2026-06-28T14:18:22.226Z