On Isaacs’ three character degrees theorem

Berkovich, Yakov

doi:10.1090/S0002-9939-97-03790-8

On Isaacs’ three character degrees theorem
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by Yakov Berkovich

Proc. Amer. Math. Soc. 125 (1997), 669-677

DOI: https://doi.org/10.1090/S0002-9939-97-03790-8

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Abstract:

Isaacs has proved that a finite group $G$ is solvable whenever there are at most three characters of pairwise distinct degrees in $\operatorname {Irr}(G)$ (Isaacs’ three character degrees theorem). In this note, using Isaacs’ result and the classification of the finite simple groups, we prove the solvability of $G$ whenever $\operatorname {Irr}(G)$ contains at most three monolithic characters of pairwise distinct degrees. §2 contains some additional results about monolithic characters.

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