Conjugacy in Houghton's Groups

Abstract

Let $n\in \mathbb{N}$. Houghton's group $H_n$ is the group of permutations of $\{1,\dots, n\}\times \mathbb{N}$, 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 $H_n$, $n\geq 2$.