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Proceedings of the American Mathematical Society

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

 
 

 

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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DOI: https://doi.org/10.1090/S0002-9939-1970-0274605-6
Keywords: Finite group, irreducible complex character, solvable group
Article copyright: © Copyright 1970 American Mathematical Society

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