Brauer characters with cyclotomic field of values

Gabriel Navarro, Pham Huu Tiep, Alexandre Turull

Research output: Contribution to journalArticle

23 Scopus citations

Abstract

It has been shown in an earlier paper [G. Navarro, Pham Huu Tiep, Rational Brauer characters, Math. Ann. 335 (2006) 675-686] that, for any odd prime p, every finite group of even order has a non-trivial rational-valued irreducible p-Brauer character. For p = 2 this statement is no longer true. In this paper we determine the possible non-abelian composition factors of finite groups without non-trivial rational-valued irreducible 2-Brauer characters. We also prove that, if p ≠ q are primes, then any finite group of order divisible by q has a non-trivial irreducible p-Brauer character with values in the cyclotomic field Q (exp (2 π i / q)).

Original languageEnglish (US)
Pages (from-to)628-635
Number of pages8
JournalJournal of Pure and Applied Algebra
Volume212
Issue number3
DOIs
StatePublished - Mar 1 2008

ASJC Scopus subject areas

  • Algebra and Number Theory

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