2 problems

Let $(X,(U_x)_{x\in X})$ be a proper Moufang set, meaning that its little projective group is not sharply $2$-transitive, and suppose that each root group $U_x$ is abelian. A quadr…

Let $T$ be a locally finite tree and let $G\leq\operatorname{Aut}(T)$ be closed, non-compact, and boundary-transitive. For distinct boundary points $\xi,\xi'\in\partial T$, write…