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 is solvable whenever there are at most three characters of pairwise distinct degrees in (Isaacs' three character degrees theorem). In this note, using Isaacs' result and the classification of the finite simple groups, we prove the solvability of whenever 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

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

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