2 problems

Let $G$ act primitively on an infinite set $\Omega$ and suppose that $G$ has a finite suborbit whose pair is also finite. The subdegrees of $G$ are then all finite. Exponential-gro…

Let $G$ be an infinite primitive permutation group whose subdegrees are all finite, and let $(m_r)$ be its lower subdegree sequence. Permutation-ends conjecture. If $(m_r)$ grows e…