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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
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.

References [Enhancements On Off] (What's this?)

  • [1] C. W. Curtis and I. Reiner, Representation theory of finite groups and associative algebras, Pure and Appl. Math., vol. XI, Interscience, New York, 1962. MR 26 #2519. MR 0144979 (26:2519)
  • [2] F. R. DeMeyer and G. J. Janusz, Finite groups with an irreducible representation of large degree, Math. Z. 108 (1969), 145-153. MR 38 #5910. MR 0237629 (38:5910)
  • [3] D. Gorenstein, Finite groups, Harper, New York, 1968. MR 38 #229. MR 0231903 (38:229)

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

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