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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On Isaacs’ three character degrees theorem
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by Yakov Berkovich PDF
Proc. Amer. Math. Soc. 125 (1997), 669-677 Request permission

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
  • 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
  • © Copyright 1997 American Mathematical Society
  • 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