Rational irreducible characters and rational conjugacy classes in finite groups

Gabriel Navarro, Pham Huu Tiep

Research output: Contribution to journalArticle

41 Scopus citations

Abstract

We prove that a finite group G has two rational-valued irreducible characters if and only if it has two rational conjugacy classes, and determine the structure of any such group. Along the way we also prove a conjecture of Gow stating that any finite group of even order has a non-trivial rationalvalued irreducible character of odd degree.

Original languageEnglish (US)
Pages (from-to)2443-2465
Number of pages23
JournalTransactions of the American Mathematical Society
Volume360
Issue number5
DOIs
StatePublished - May 1 2008

Keywords

  • Rational conjugacy class
  • Rational irreducible character

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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