On the vanishing prime graph of finite groups

被引：31

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, Fac Matemat, Dept Algebra, E-46100 Valencia, Spain

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

来源：

JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES | 2010年 / 82卷

关键词：

IRREDUCIBLE CHARACTERS; COMPONENTS;

D O I：

10.1112/jlms/jdq021

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let G be a finite group. An element g is an element of G is called a vanishing element of G if there exists an irreducible complex character chi of G such that chi(g) = 0. In this paper we study the vanishing prime graph Gamma(G), whose vertices are the prime numbers dividing the orders of some vanishing element of G, and two distinct vertices p and q are adjacent if and only if G has a vanishing element of order divisible by pq. Among other things we prove that, similarly to what holds for the prime graph of G, the graph Gamma(G) has at most six connected components.

引用

页码：167 / 183

页数：17

共 15 条

[1] Finite groups whose irreducible characters vanish only on p-elements [J].