Hyperbolic groups containing subgroups of type $\mathscr{F}_3$ not $\mathscr{F}_4$
Hyperbolic groups containing subgroups of type $\mathscr{F}_3$ not $\mathscr{F}_4$
We give examples of hyperbolic groups which contain subgroups that are of type $\mathscr{F}_{3}$ but not of type $\mathscr{F}_{4}$. These groups are obtained by Dehn filling starting from a non-uniform lattice in ${\rm PO}(8,1)$ which was previously studied by Italiano, Martelli and Migliorini.