Characters of p'-degree and Thompson's character degree theorem

Nguyen Ngoc Hung

Characters of p'-degree and Thompson's character degree theorem

Group Theory 2015-06-23 v1 Representation Theory

Authors: Nguyen Ngoc Hung

Abstract

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 $p$ , then $G$ has a normal $p$ -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.

Keywords

character degrees finite groups thompson's theorem p-complement irreducible characters character values p'-degrees

Cite

@article{arxiv.1506.06450,
  title  = {Characters of p'-degree and Thompson's character degree theorem},
  author = {Nguyen Ngoc Hung},
  journal= {arXiv preprint arXiv:1506.06450},
  year   = {2015}
}

Comments

23 pages

Characters of p'-degree and Thompson's character degree theorem

Abstract

Keywords

Cite

Comments

Related papers