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A classical theorem of John Thompson on character degrees asserts that if thedegree of every ordinary irreducible character of a finite group $G$ is 1 ordivisible by a prime $p$, then $G$ has a normal $p$-complement. We obtain asignificant improvement of this result by considering the average of$p'$-degrees of irreducible characters. We also consider fields of charactervalues and prove several improvements of earlier related results.

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