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.
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页码：345 / 352
页数：8
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