Search results for "Irreducible character"

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Some problems in number theory that arise from group theory

2021

In this expository paper, we present several open problems in number theory that have arisen while doing research in group theory. These problems are on arithmetical functions or partitions. Solving some of these problems would allow to solve some open problem in group theory.

AlgebraIrreducible characterNumber theoryArithmetical functionGeneral MathematicsOpen problemArithmetic functionSymmetric groupGroup theoryCharacter degreeMathematicsPartition
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On the orders of zeros of irreducible characters

2009

Let G be a finite group and p a prime number. We say that an element g in G is a vanishing element of G if there exists an irreducible character χ of G such that χ (g) = 0. The main result of this paper shows that, if G does not have any vanishing element of p-power order, then G has a normal Sylow p-subgroup. Also, we prove that this result is a generalization of some classical theorems in Character Theory of finite groups. © 2008 Elsevier Inc. All rights reserved.

Discrete mathematicsFinite groupPure mathematicsBrauer's theorem on induced charactersAlgebra and Number Theoryirreducible character zeroCharacter theorySylow theoremsPrime numberIrreducible elementFinite groupsCharacter (mathematics)Order (group theory)Zeros of charactersCharactersMathematics
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