Prime Divisibility Among Degrees of Solvable Groups

Let G be a finite, nonabelian, solvable group. Following work by D. Benjamin, we conjecture that some prime must divide at least a third of the irreducible character degrees of G. Benjamin was able to show the conjecture is true if all primes divide at most 3 degrees. We extend this result by showin...

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Bibliographic Details
Published in:Communications in algebra 2004-12, Vol.32 (9), p.3391-3402
Main Author: McVey, John K.
Format: Article
Language:English
Subjects:
Character degree
Solvable group
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Summary:Let G be a finite, nonabelian, solvable group. Following work by D. Benjamin, we conjecture that some prime must divide at least a third of the irreducible character degrees of G. Benjamin was able to show the conjecture is true if all primes divide at most 3 degrees. We extend this result by showing if primes divide at most 4 degrees, then G has at most 12 degrees. We also present an example showing our result is best possible.
ISSN:0092-7872
1532-4125
DOI:10.1081/AGB-120039553