The NIP conjecture for omega-categorical groups

Let $G$ be a group whose first-order theory is NIP, and suppose that $G$ is $\omega$-categorical, meaning that its theory has at most one countable model up to isomorphism. A group is nilpotent-by-finite if it has a nilpotent normal subgroup of finite index.

NIP conjecture for omega-categorical groups. Every $\omega$-categorical group with NIP is nilpotent-by-finite.

This would extend the known result that omega-categorical stable groups are nilpotent-by-finite. The conjecture concerns the broader NIP setting and is presented as an open problem.