Semisimple Groups

Abstract

Abstract We deal here with the structure of semisimple groups and the definition of the generalized Fitting subgroup F* (G) in our context. This is a notion which is used constantly in the analysis of finite simple groups and may be expected to play a parallel role in the context of connected simple groups of finite Morley rank, notably in connection with the solution of Problem C of Chapter B. As the most concrete applications of the general theory given here are to rather small groups, in Chapter 14, we do not yet have solid evidence that the arguments parallel to the finite case go through here; but barring major surprises this notion should turn out to be a workhorse for the further development of the theory. In any case both the Fitting subgroup and the socle in the definable versions used here have proved their utility already, and from that point it is a small step to the generalized Fitting subgroup.