Minimal connected simple groups of finite Morley rank with strongly embedded subgroups

Let G be a simple K∗-group of finite Morley rank of odd type which is not algebraic. Then G has Prüfer 2-rank at most two. This improves on an earlier result of the second and third authors for the tame case. In the critical case G is minimal connected simple of odd type with a proper definable strongly embedded subgroup. The bulk of the analysis relies on the first author's theory of 0-unipotence and the related 0-Sylow subgroup theory, as well as the so-called Bender method adapted to this context.