Minimal Connected Simple Groups of Finite Morley Rank with Strongly Embedded Subgroups

The Algebraicity Conjecture states that a simple group of finite Morley rank should be isomorphic with an algebraic group. A program initiated by Borovik aims at controlling the 2-local structure in a hypothetical minimal counterexample to the Algebraicity Conjecture. There is now a large body of work on this program. A fundamental division arises at the outset, according to the structure of a Sylow 2subgroup. In algebraic groups this structure depends primarily on the characteristic of the base field. In groups of finite Morley rank in general, in addition to the even and odd type groups, which correspond naturally to the cases of characteristic two or not two, respectively, we have two more cases, called mixed and degenerate type. In the degenerate case the Sylow 2-subgroup is finite. The cases of even and mixed type groups are well in hand, and it seems that work in course of publication will show that the simple groups of finite Morley rank of these two types are algebraic. Work on degenerate type has hardly begun, though recently some interesting approaches have emerged. We deal here with odd type groups exclusively. In this context, the “generic” case is generally considered to be that of groups of Prüfer 2-rank three or more. The following result enables us to complete the analysis of the generic case.