Primes dividing the degrees of the real characters

被引：52

作者：

Dolfi, Silvio ^{[2
]}

Navarro, Gabriel ^{[1
]}

Tiep, Pham Huu ^{[3
]}

机构：

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

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

[3] Univ Florida, Dept Math, Gainesville, FL 32611 USA

来源：

MATHEMATISCHE ZEITSCHRIFT | 2008年 / 259卷 / 04期

基金：

美国国家科学基金会;

关键词：

D O I：

10.1007/s00209-007-0247-8

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 all complex irreducible characters of G. The Ito-Michler Theorem asserts that if a prime p does not divide the degree of any chi is an element of Irr(G) then a Sylow p-subgroup P of G is normal in G. We prove a real-valued version of this theorem, where instead of Irr(G) we only consider the subset Irr(rv)(G) consisting of all real-valued irreducible characters of G. We also prove that the character degree graph associated to Irr(rv)(G) has at most 3 connected components. Similar results for the set of real conjugacy classes of G have also been obtained.

引用

页码：755 / 774

页数：20

共 29 条

[1] On the Navarro-Willems conjecture for blocks of finite groups [J].