Revista Matemática Iberoamericana

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Volume 33, Issue 1, 2017, pp. 117–138
DOI: 10.4171/RMI/929

Published online: 2017-02-22

Characters of $p’$-degree and Thompson’s character degree theorem

Nguyen Ngoc Hung[1]

(1) University of Akron, USA

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: Finite groups, character degrees, Thompson’s theorem, normal $p$-complement, solvability, $p$-nilpotency

Hung Nguyen Ngoc: Characters of $p’$-degree and Thompson’s character degree theorem. Rev. Mat. Iberoam. 33 (2017), 117-138. doi: 10.4171/RMI/929