Weak Tits alternative for groups acting geometrically on buildings

Abstract

We show that if a group $G$ acts geometrically by type-preserving automorphisms on a building, then $G$ satisfies the weak Tits alternative, namely, that $G$ is either virtually abelian or contains a non-abelian free group.

16 pages, 5 figures. Published in press in Journal of Algebra at https://doi.org/10.1016/j.jalgebra.2024.05.015