3 problems

A BMW group is a group acting on a product of two regular trees, and a BMW group of degree $(m,n)$ has tree factors of degrees $m$ and $n$. In the range $n>m^5$, consider the rando…

Let $T_d$ be the $d$-regular tree, let $\Omega$ be a finite set, and let $F\leq\operatorname{Sym}(\Omega)$ be semiprimitive, meaning that every normal subgroup of $F$ is either tra…

Type I conjecture. Then $G$ is a type ${\rm I}$ group.