Prime Divisibility Among Degrees of Solvable Groups

Abstract

Let G be a finite, nonabelian, solvable group. Following work by D. Benjamin, we conjecture that some prime must divide at least a third of the irreducible character degrees of G. Benjamin was able to show the conjecture is true if all primes divide at most 3 degrees. We extend this result by showing if primes divide at most 4 degrees, then G has at most 12 degrees. We also present an example showing our result is best possible.