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On Isaacs' three character degrees theorem

Author: Yakov Berkovich
Journal: Proc. Amer. Math. Soc. 125 (1997), 669-677
MSC (1991): Primary 20C15
MathSciNet review: 1376750
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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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Additional Information

Yakov Berkovich
Affiliation: Department of Mathematics and Computer Science, University of Haifa, Haifa 31905, Israel

Keywords: Monolith, monolithic character, automorphism group, classification of finite simple groups
Received by editor(s): September 5, 1995
Additional Notes: The author was supported in part by the Ministry of Absorption of Israel
Communicated by: Ronald M. Solomon
Article copyright: © Copyright 1997 American Mathematical Society