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2013 Zeros of real irreducible characters of finite groups
Selena Marinelli, Pham Tiep
Algebra Number Theory 7(3): 567-593 (2013). DOI: 10.2140/ant.2013.7.567

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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Selena Marinelli. Pham Tiep. "Zeros of real irreducible characters of finite groups." Algebra Number Theory 7 (3) 567 - 593, 2013. https://doi.org/10.2140/ant.2013.7.567

Information

Received: 21 March 2011; Revised: 2 February 2012; Accepted: 16 March 2012; Published: 2013
First available in Project Euclid: 20 December 2017

zbMATH: 1295.20006
MathSciNet: MR3095221
Digital Object Identifier: 10.2140/ant.2013.7.567

Subjects:
Primary: 20C15
Secondary: 20C33

Rights: Copyright © 2013 Mathematical Sciences Publishers

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