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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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Groups with an irreducible character of large degree are solvable


Author: Frank DeMeyer
Journal: Proc. Amer. Math. Soc. 25 (1970), 615-617
MSC: Primary 20.80
DOI: https://doi.org/10.1090/S0002-9939-1970-0274605-6
MathSciNet review: 0274605
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Abstract: The degree of an irreducible complex character afforded by a finite group is bounded above by the index of an abelian normal subgroup and by the square root of the index of the center. Whenever a finite group affords an irreducible character whose degree achieves these two upper bounds the group must be solvable.


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Keywords: Finite group, irreducible complex character, solvable group
Article copyright: © Copyright 1970 American Mathematical Society