Zeros of real irreducible characters of finite groups

Selena Marinelli; Pham Huu Tiep

doi:10.2140/ant.2013.7.567

Zeros of real irreducible characters of finite groups

Selena Marinelli, Pham Huu Tiep

Research output: Contribution to journal › Article › peer-review

12 Scopus citations

Abstract

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.

Original language	English (US)
Pages (from-to)	567-593
Number of pages	27
Journal	Algebra and Number Theory
Volume	7
Issue number	3
DOIs	https://doi.org/10.2140/ant.2013.7.567
State	Published - 2013
Externally published	Yes

Keywords

Frobenius-Schur indicator
Nonvanishing element
Real irreducible character

ASJC Scopus subject areas

Algebra and Number Theory

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10.2140/ant.2013.7.567

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abstract = "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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AU - Tiep, Pham Huu

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AB - 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.

KW - Frobenius-Schur indicator

KW - Nonvanishing element

KW - Real irreducible character

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Zeros of real irreducible characters of finite groups

Abstract

Keywords

ASJC Scopus subject areas

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