Twisted Conjugacy in Houghton's groups

Charles Cox

Published 2014-10-26Version 1

For a fixed $n\ge2$, Houghton's group $H_n$ consists of bijections of $X_n=\{1,\ldots,n\} \times \mathbb{N}$ that are 'eventually translations' of each copy of $\mathbb{N}$. These groups were recently shown to have solvable conjugacy problem. In general this does not imply that all finite extensions and finite index subgroups have solvable conjugacy problem. In this note we show that, for $H_n$, it does.