Conjugacy in Houghton's Groups

Yago Antolín, José Burillo, Armando Martino

Published 2013-05-09, updated 2014-06-30Version 2

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 $H_n$, $n\geq 2$.