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 | References | Similar Articles | Additional Information
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.
- Charles W. Curtis and Irving Reiner, Representation theory of finite groups and associative algebras, Pure and Applied Mathematics, Vol. XI, Interscience Publishers, a division of John Wiley & Sons, New York-London, 1962. MR 0144979
- Frank R. DeMeyer and Gerald J. Janusz, Finite groups with an irreducible representation of large degree, Math. Z. 108 (1969), 145–153. MR 237629, DOI https://doi.org/10.1007/BF01114468
- Daniel Gorenstein, Finite groups, Harper & Row, Publishers, New York-London, 1968. MR 0231903
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Keywords:
Finite group,
irreducible complex character,
solvable group
Article copyright:
© Copyright 1970
American Mathematical Society