Automorphisms of non-spherical buildings have unbounded displacement

Abstract

If $\varphi$ is a nontrivial automorphism of a thick building $\mathrm{\Delta }$ of purely infinite type, we prove that there is no bound on the distance that $\varphi$ moves a chamber. This has the following group-theoretic consequence: If $G$ is a group of automorphisms of $\mathrm{\Delta }$ with bounded quotient, then the center of $G$ is trivial.