Zeros of real irreducible characters of finite groups

Selena Marinelli, Pham Huu Tiep

Research output: Contribution to journalArticlepeer-review

11 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 languageEnglish (US)
Pages (from-to)567-593
Number of pages27
JournalAlgebra and Number Theory
Volume7
Issue number3
DOIs
StatePublished - Sep 9 2013

Keywords

  • Frobenius-Schur indicator
  • Nonvanishing element
  • Real irreducible character

ASJC Scopus subject areas

  • Algebra and Number Theory

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