Nonexistence of regular-type primitive permutation groups

Show that connected primitive permutation groups of finite Morley rank of regular type do not exist.

Background

Regular-type primitive actions would arise from a connected group acting irreducibly on a simple regular normal subgroup. Their existence has been questioned since the Macpherson–Pillay classification and is tied to broader algebraicity expectations.

Ruling out this case would simplify the landscape of primitive permutation groups of finite Morley rank and reinforce the analogy with the classical O’Nan–Scott framework.