6533b873fe1ef96bd12d4d82

RESEARCH PRODUCT

On the orders of zeros of irreducible characters

Silvio DolfiPablo SpigaEmanuele PacificiLucia Sanus

subject

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

description

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.

yearjournalcountryeditionlanguage
2009-01-01
10.1016/j.jalgebra.2008.10.004http://hdl.handle.net/10281/22104