On the orders of zeros of irreducible characters

JOURNAL OF ALGEBRA

卷:321

Article

Dolfi, Silvio¹  Pacifici, Emanuele²  Sanus, Lucia³  Spiga, Pablo⁴ 

[1] Univ Florence, Dipartimento Matemat U Dini, I-50134 Florence, Italy

[2] Univ Milan, Dipartimento Matemat F Enriques, I-20133 Milan, Italy

[3] Univ Valencia, Dept Algebra, Fac Matemat, E-46100 Valencia, Spain

[4] Univ Padua, Dipartimento Matemat Pura & Applicata, I-35121 Padua, Italy

关键词: Finite groups;    Characters;    Zeros of characters;   

DOI  :  10.1016/j.jalgebra.2008.10.004

来源: Elsevier

【 摘 要 】

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 X of G such that X(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. (c) 2008 Elsevier Inc. All rights reserved.

【 授权许可】

Free