Regular Orbits in the Quasiprimitve Case

We begin our study of large orbit theorems, by proving the existence of regular orbits for solvable quasiprimitive groups with a large value of e. We see our first of several important results bounding the size of certain fixed point subspaces, and we see how to use those bounds to generate regular orbits. We end with a discussion of the work of the second author that classifies the solvable primitive groups that do not have regular orbits.