Primitive pairs of p-solvable groups

The subgroup structure of a finite group G can be quite complex. However, in the presence of a group R of automorphisms of G and provided we consider only certain subgroups related to R, the situation appears much simpler. The purpose of this article is to provide concrete results in this direction. These results have been applied to give a new proof of the Solvable Signalizer Functor Theorem.