VARIATIONS ON THOMPSON'S CHARACTER DEGREE THEOREM

Abstract

If P is a Sylow- p -subgroup of a finite p -solvable group G , we prove that G^\prime \cap \bf{N}_G(P) \subseteq {P} if and only if p divides the degree of every irreducible non-linear p -Brauer character of G. More generally if π is a set of primes containing p and G is π-separable, we give necessary and sufficient group theoretic conditions for the degree of every irreducible non-linear p -Brauer character to be divisible by some prime in π. This can also be applied to degrees of ordinary characters.