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BOUNDING THE NUMBER OF IRREDUCIBLE CHARACTER DEGREES OF A FINITE GROUP IN TERMS OF THE LARGEST DEGREE

2013

We conjecture that the number of irreducible character degrees of a finite group is bounded in terms of the number of prime factors (counting multiplicities) of the largest character degree. We prove that this conjecture holds when the largest character degree is prime and when the character degree graph is disconnected.

CombinatoricsDiscrete mathematicsFinite groupOrientation characterAlgebra and Number TheoryCharacter (mathematics)Degree (graph theory)Character tableApplied MathematicsPrime factorCharacter groupPrime (order theory)MathematicsJournal of Algebra and Its Applications
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