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 -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 .
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}
}