Resumen de Characters of p′-degree and Thompson’s character degree theorem

Nguyen Ngoc Hung

• A classical theorem of John Thompson on character degrees asserts that if the degree of every ordinary irreducible character of a finite group G is 1 or divisible by a prime pp, then G has a normal pp-complement. We obtain a significant improvement of this result by considering the average of p′-degrees of irreducible characters. We also consider fields of character values and prove several improvements of earlier related results.