On the orders of zeros of irreducible characters

被引：43

作者：

Dolfi, Silvio ^{[1
]}

Pacifici, Emanuele ^{[2
]}

Sanus, Lucia ^{[3
]}

Spiga, Pablo ^{[4
]}

机构：

[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

来源：

JOURNAL OF ALGEBRA | 2009年 / 321卷 / 01期

关键词：

Finite groups; Characters; Zeros of characters; FINITE SIMPLE-GROUPS; DEFECT ZERO; P-BLOCKS; LIE TYPE;

D O I：

10.1016/j.jalgebra.2008.10.004

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

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.

引用

页码：345 / 352

页数：8

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