Nonexistence of faithful irreducible actions on simple groups (beyond conjugation)

Show that no connected group M of finite Morley rank can act faithfully and irreducibly by automorphisms on a simple group S of finite Morley rank unless M equals S acting on itself by conjugation.

Background

Primitive groups of regular type would require a connected group to act irreducibly on a simple group via automorphisms, which is expected to be impossible except for the conjugation action by the group itself.

Establishing this would rule out regular-type primitive permutation groups and would follow from the general Cherlin–Zilber algebraicity conjecture.