One variable equations over the lamplighter group
Group Theory
2025-12-01 v1 Combinatorics
Abstract
We prove that one variable equations in the lamplighter group are decidable and describe an algorithm for solving such equations. The algorithm has super-exponential time complexity in the worst case. We also show that, for most equations, decidability can be determined in nearly quadratic time; that is, the problem admits a nearly quadratic-time solution in the generic case.
Cite
@article{arxiv.2511.23006,
title = {One variable equations over the lamplighter group},
author = {Alexander Ushakov and Yankun Wang},
journal= {arXiv preprint arXiv:2511.23006},
year = {2025}
}