Ping-pong in the projective plane over a nonarchimedean field

Sami Douba, Dmitry Kubrak, Konstantinos Tsouvalas

We show that any lattice in ${\mathrm{SL}}_3(k)$, where $k$ is a nonarchimedean local field, contains an undistorted subgroup isomorphic to the free product ${\mathbb{Z}}^2\ast \mathbb{Z}$…