Primes dividing character degrees and character orbit sizes-Reference-Cited by-同舟云学术

Primes dividing character degrees and character orbit sizes

Published:1987 Issue:2 Volume:101 Page:219-225
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Gluck David

Abstract

We consider an abelian group A A which acts faithfully and coprimely on a solvable group G G . We show that some A A -orbit on Irr ⁡ ( G ) \operatorname {Irr}(G) must have cardinality divisible by almost half the primes in π ( A ) \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.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1987-101-02/S0002-9939-1987-0902531-8/S0002-9939-1987-0902531-8.pdf

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2. Defect groups and character heights in blocks of solvable groups. II;Gluck, David;J. Algebra,1984

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4. Pure and Applied Mathematics, No. 69;Isaacs, I. Martin,1976

5. Solvable groups character degrees and sets of primes;Isaacs, I. M.;J. Algebra,1986

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