Other Applications of Large Orbit Theorems

In our final chapter we discuss (with somewhat less detail) other applications of large orbit theorems to the study of solvable groups. We begin by discussing certain induction and restriction theorems that require a variation of Dolfi’s large orbit theorem from Chapter 8. We then discuss a result of Moreto and Wolf that determines that number of characters needed to “cover” the order of the solvable group G. In the last section we discuss, without proof, a number of other uses for large orbit theorems in the study of solvable groups, including character degrees, nilpotent blocks, and zeros of characters.