In a 1995 paper by Ali Nesin, "Permutation groups of finite Morley rank", the following conjecture is mentioned:

**Conjecture 5** An infinite Zassenhaus group $G$ of finite Morley rank is isomorphic to $\operatorname{PSL}_2(K)$ for some algebraically closed field $K$. Furthermore the action of $G$ is isomorphic to the action of $\operatorname{PSL}_2(K)$ acting naturally on the projective line.

Searching the web for any advances in this conjecture were fruitless, and I even couldn't find another mentioning of this conjecture. My question is whether it is still open, and if so - what are the current, if any, settings in which a variation of this is known. In particular I'm interested in the variation where $G\leq\operatorname{GL}_n(F)$ is a Zassenhaus group, or even a more restrictive setting, where $G\leq\operatorname{GL}_n(F)$ is a sharply $3$-transitive group.

I know that a variation of this result was proved by Tits in 1941, when he showed that a a locally compact connected sharply 3-transitive group is isomorphic to $\operatorname{PSL}_2(\mathbb{R})$ or $\operatorname{PSL}_2(\mathbb{C})$ (there where no assumptions on the Morley rank, so the field could be non algebraically closed)