Conjugacy in Houghton's groups

Abstract

Let $n\in {\mathbb N}$. Houghton's group $H_n$ is the group of permutations of $\{1,\dotsc, n\}\times {\mathbb N}$, that eventually act as a translation in each copy of ${\mathbb N}$. We prove the solvability of the conjugacy problem and conjugator search problem for $H_n$, $n\geq 2$.