Every lattice in SL_3(k) over a nonarchimedean local field k contains an undistorted subgroup isomorphic to Z^2 * Z, yielding new discrete subgroups not virtually isomorphic to lattices.
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Ping-pong in the projective plane over a nonarchimedean field
Every lattice in SL_3(k) over a nonarchimedean local field k contains an undistorted subgroup isomorphic to Z^2 * Z, yielding new discrete subgroups not virtually isomorphic to lattices.