Finiteness properties of Subgroups of Houghton Groups of full Hirsch length

Charles Garnet Cox, Peter Kropholler, Armando Martino

In the 1980's K.S. Brown proved that the Houghton group $H_n$ is of type $F_{n-1}$ but not ${\mathrm{FP}}_n$. We show that, provided $n\ge 3$, the same conclusion…