2 papers
math.GR2026
One-variable equations over the lamplighter group
Alexander Ushakov, Yankun Wang
We study one-variable equations over the lamplighter group $\MZ_2 \wr \MZ$. While the decidability of arbitrary equations over remains open, we prove that the Diophantine pro…
math.GR2025
One variable equations over the lamplighter group
Alexander Ushakov, Yankun Wang
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…