On Isaacs’ three character degrees theorem

Author:
Yakov Berkovich

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

MSC (1991):
Primary 20C15

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

MathSciNet review:
1376750

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Abstract | References | Similar Articles | Additional Information

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