7 problems

A Moufang set is a permutation structure with associated root groups; a Moufang set is proper when its associated group is not sharply $2$-transitive. For a quadratic Jordan divisi…

Nilpotence conjecture. The root groups of every proper Moufang set are nilpotent.

Quadratic Jordan algebra conjecture. Every proper Moufang set with abelian root groups comes from a quadratic Jordan division algebra.

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…

A Moufang set is a pair $(X,(U_x)_{x\in X})$ consisting of a set $X$ and root groups $U_x\leq\operatorname{Sym}(X)$ such that each $U_x$ fixes $x$, acts regularly on…

Let $\operatorname{\mathbb{M}}$ be an infinite proper Moufang set of finite Morley rank. For a field $F$, let $\operatorname{\mathbb{M}}(F)$ denote the associated Moufang set, and…

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…