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.
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页码：567 / 593
页数：27
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