Non-vanishing elements of finite groups

被引：18

作者：

Dolfi, Silvio ^{[2
]}

Navarro, Gabriel ^{[3
]}

Pacifici, Emanuele ^{[1
]}

Sanus, Lucia ^{[3
]}

Tiep, Pham Huu ^{[4
]}

机构：

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

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

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

[4] Univ Arizona, Dept Math, Tucson, AZ 85721 USA

来源：

JOURNAL OF ALGEBRA | 2010年 / 323卷 / 02期

基金：

美国国家科学基金会;

关键词：

Finite groups; Characters; Zeros of characters; CHARACTERS;

D O I：

10.1016/j.jalgebra.2009.08.014

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let 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 chi in Irr(G), we have chi (x) not equal 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. (C) 2009 Elsevier Inc. All rights reserved.

引用

页码：540 / 545

页数：6

共 15 条

[1]

Carter R. W., 1985, Pure and Applied Mathematics (New York)

[2]

Digne F., 1991, London Math. Soc. Student Texts, V21

[3] ON FINITE RATIONAL GROUPS AND RELATED TOPICS [J].

FEIT, W ;

SEITZ, GM .

ILLINOIS JOURNAL OF MATHEMATICS, 1989, 33 (01) :103-131

[4]

GLUCK D, 1983, CAN J MATH, V35, P59, DOI 10.4153/CJM-1983-005-2

[5]

Gorenstein D., 1994, Math. Surveys Monogr., V3

[6] Defect zero p-blocks for finite simple groups [J].

Granville, A ;

Ono, K .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1996, 348 (01) :331-347

[7]

Huppert B., 1967, Endliche Gruppen I

[8]

Isaacs I. M., 2006, CHARACTER THEORY FIN

[9] Finite group elements where no irreducible character vanishes [J].

Isaacs, IM ;

Navarro, G ;

Wolf, TR .

JOURNAL OF ALGEBRA, 1999, 222 (02) :413-423

[10]

LUSZTIG G, 1984, ANN MATH STUD, pR3

← 1 2 →