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 F3 but not of type F4. These groups are obtained by Dehn filling starting from a non-uniform lattice in PO(8, 1) which was previously studied by Italiano, Martelli and Migliorini.

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