Solvable Quasiprimitive Groups

In this chapter we discuss in great depth the structure of solvable quasiprimitive groups. Using Hall’s theorem on p-groups from Chapter 3 and some basic group theory, we can say a great deal about the subgroup structure of a solvable quasiprimitive group, and we introduce the crucial parameter e. We study solvable quasiprimitive groups that have a small value of e. We then examine maximal solvable primitive groups, and end with a discussion of prototypical large orbit theorems for abelian or nilpotent groups.