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

Nguyen Ngoc Hung

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arXiv · 1506.06450

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

Nguyen Ngoc Hung

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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.

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Nguyen Ngoc Hung. 2015-06-22. Characters of p'-degree and Thompson's character degree theorem. https://arxiv.org/abs/1506.06450

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