Search results for "Zeros of characters"

showing 2 items of 2 documents

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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Non-vanishing elements of finite groups

2010

AbstractLet G be a finite group, and let Irr(G) denote the set of irreducible complex characters of G. An element x of G is non-vanishing if, for every χ in Irr(G), we have χ(x)≠0. We prove that, if x is a non-vanishing element of G and the order of x is coprime to 6, then x lies in the Fitting subgroup of G.

Finite groupBrauer's theorem on induced charactersAlgebra and Number TheoryCoprime integers010102 general mathematics0102 computer and information sciences01 natural sciencesFitting subgroupFinite groupsCombinatorics010201 computation theory & mathematicsOrder (group theory)Zeros of charactersCharacters0101 mathematicsElement (category theory)MathematicsJournal of Algebra
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