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arXiv · 2401.08589

Quadratic equations in the lamplighter group

Alexander Ushakov·Chloe Weiers
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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 $\mathbf{NP}$-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 $\mathbf{XP}$.

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Alexander Ushakov, Chloe Weiers. 2023-11-13. Quadratic equations in the lamplighter group. https://arxiv.org/abs/2401.08589

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