Zeros of real irreducible characters of finite groups

被引：13

作者：

Marinelli, Selena ^{[1
]}

Tiep, Pham Huu ^{[2
]}

机构：

[1] Univ Pisa, Dipartimento Matemat L Tonelli, I-56127 Pisa, Italy

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

来源：

ALGEBRA & NUMBER THEORY | 2013年 / 7卷 / 03期

基金：

美国国家科学基金会;

关键词：

real irreducible character; nonvanishing element; Frobenius-Schur indicator; VANISHING PRIME GRAPH; BRAUER CHARACTERS; CONJUGACY CLASSES; CLASS SIZES; REPRESENTATIONS; SUBGROUPS;

D O I：

10.2140/ant.2013.7.567

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that if all real-valued irreducible characters of a finite group G with Frobenius-Schur indicator 1 are nonzero at all 2-elements of G, then G has a normal Sylow 2-subgroup. This result generalizes the celebrated Ito-Michler theorem (for the prime 2 and real, absolutely irreducible, representations), as well as several recent results on nonvanishing elements of finite groups.

引用

页码：567 / 593

页数：27

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