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arXiv · 2511.23006

One variable equations over the lamplighter group

Alexander Ushakov·Yankun Wang
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Abstract

We prove that one variable equations in the lamplighter group $\MZ_2\wr \MZ$ 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.

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Alexander Ushakov, Yankun Wang. 2025-11-28. One variable equations over the lamplighter group. https://arxiv.org/abs/2511.23006

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