Selflessness, MIF and opposition in groups acting on exotic buildings

Corentin Le Bars, Elyasheev Leibtag, Itamar Vigdorovich

We prove that groups acting freely and cocompactly on (possibly exotic) affine buildings of type ${\tilde{A}}_2$ and ${\tilde{C}}_2$ are mixed-identity free and have selfless reduced $C…