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 which acts faithfully and coprimely on a solvable group . We show that some -orbit on must have cardinality divisible by almost half the primes in . 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:
https://doi.org/10.1090/S0002-9939-1987-0902531-8

Article copyright:
© Copyright 1987
American Mathematical Society