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

School of Arts and Sciences, Mathematics

Research output: Contribution to journal › Article

8 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 - Sep 9 2013

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All Science Journal Classification (ASJC) codes

Algebra and Number Theory

Keywords

Frobenius-Schur indicator
Nonvanishing element
Real irreducible character

Cite this

Marinelli, S., & Tiep, P. H. (2013). Zeros of real irreducible characters of finite groups. Algebra and Number Theory, 7(3), 567-593. https://doi.org/10.2140/ant.2013.7.567

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Access to Document

10.2140/ant.2013.7.567