A signalizer functor theorem for groups of finite Morley rank

Abstract

There is a longstanding conjecture, due to Gregory Cherlin and Boris Zilber, that all simple groups of finite Morley rank are simple algebraic groups. One of the major theorems in the area is Borovik's trichotomy theorem. The "trichotomy" here is a case division of the minimal counterexamples within odd type, i.e. groups with a divisibble connected component of the Sylow 2-subgroup. We introduce a charateristic zero notion of unipotence which can be used to obtain a connected nilpotent signalizer functor from any sufficiently non-trivial solvable signalizer functor. This result plugs seamlessly into Borovik's work to eliminate the assumption of tameness from his trichotomy theorem for odd type groups. This work also provides us with a form of Borovik's theorem for degenerate type groups.