A classical theorem of John Thompson on character degrees asserts that if the degree of every ordinary irreducible character of a finite group is 1 or divisible by a prime , then has a normal -complement. We obtain a significant improvement of this result by considering the average of -degrees of irreducible characters. We also consider fields of character values and prove several improvements of earlier related results.
Cite this article
Nguyen Ngoc Hung, Characters of -degree and Thompson’s character degree theorem. Rev. Mat. Iberoam. 33 (2017), no. 1, pp. 117–138DOI 10.4171/RMI/929