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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Primes dividing character degrees and character orbit sizes


Author: David Gluck
Journal: Proc. Amer. Math. Soc. 101 (1987), 219-225
MSC: Primary 20C15
MathSciNet review: 902531
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Abstract: We consider an abelian group $ A$ which acts faithfully and coprimely on a solvable group $ G$. We show that some $ A$-orbit on $ \operatorname{Irr}(G)$ must have cardinality divisible by almost half the primes in $ \pi (A)$. As a corollary, we improve a recent result of I. M. Isaacs concerning the maximum number of primes dividing any one character degree of a solvable group.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1987-0902531-8
PII: S 0002-9939(1987)0902531-8
Article copyright: © Copyright 1987 American Mathematical Society