A classical theorem of John Thompson on character degrees states that if the degree of any complex irreducible character of a finite group G is 1 or divisible by a prime p, then G has a normal p-complement. In this paper, we consider fields of values of characters and prove some improvements of this result. © 2010 Elsevier Inc.
Navarro, G., & Tiep, P. H. (2010). Degrees of rational characters of finite groups. Advances in Mathematics, 224(3), 1121–1142. https://doi.org/10.1016/j.aim.2009.12.023