Search results for "Character group"

showing 6 items of 6 documents

Degrees of Characters and Values on Prime Order Elements

2008

Two irreducible characters of a finite group with the same value on prime elements have the same degree.

AlgebraFinite groupPure mathematicsAlgebra and Number TheoryMathematics::Number TheoryPrime elementDegree (angle)Mathematics::Representation TheoryValue (mathematics)Character groupMathematicsCommunications in Algebra
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Groups with exactly one irreducible character of degree divisible byp

2014

Let [math] be a prime. We characterize those finite groups which have precisely one irreducible character of degree divisible by [math] .

AlgebraPure mathematicsAlgebra and Number TheoryCharacter (mathematics)character degreesCharacter tableDegree (graph theory)characters20C15Character groupfinite groupsMathematicsAlgebra & Number Theory
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Degrees of irreducible characters of the symmetric group and exponential growth

2015

We consider sequences of degrees of ordinary irreducible S n S_n - characters. We assume that the corresponding Young diagrams have rows and columns bounded by some linear function of n n with leading coefficient less than one. We show that any such sequence has at least exponential growth and we compute an explicit bound.

CharacterPower sum symmetric polynomialGeneral MathematicsApplied MathematicsMathematicsofComputing_GENERALComplete homogeneous symmetric polynomialExponential polynomialExponential growthCombinatoricsRepresentation theory of the symmetric groupSymmetric groupElementary symmetric polynomialMathematics (all)Ring of symmetric functionsCharacter groupSymmetric groupMathematics
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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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Rational irreducible characters and rational conjugacy classes in finite groups

2007

We prove that a finite group G G has two rational-valued irreducible characters if and only if it has two rational conjugacy classes, and determine the structure of any such group. Along the way we also prove a conjecture of Gow stating that any finite group of even order has a non-trivial rational-valued irreducible character of odd degree.

Computer Science::Machine LearningFinite groupApplied MathematicsGeneral MathematicsIrreducible elementComputer Science::Digital LibrariesIrreducible fractionCombinatoricsStatistics::Machine LearningConjugacy classCharacter (mathematics)Character tableComputer Science::Mathematical SoftwareOrder (group theory)Character groupMathematicsTransactions of the American Mathematical Society
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Finite groups with real-valued irreducible characters of prime degree

2008

Abstract In this paper we describe the structure of finite groups whose real-valued nonlinear irreducible characters have all prime degree. The more general situation in which the real-valued irreducible characters of a finite group have all squarefree degree is also considered.

Finite groupReal charactersBrauer's theorem on induced charactersAlgebra and Number TheoryDegree (graph theory)Mathematics::Number TheoryStructure (category theory)Prime elementSquare-free integerCharacter degreesCombinatoricsCharacter tableMathematics::Representation TheoryCharacter groupMathematicsJournal of Algebra
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