p-rational characters and self-normalizing sylowp-subgroups

Gabriel Navarro, Phamhuu Tiep, Alexandre Turull

Research output: Contribution to journalArticlepeer-review

28 Scopus citations

Abstract

Let G be a finite group, p a prime, and P a Sylow p-subgroup of G. Several recent refinements of the McKay conjecture suggest that there should exist a bijection between the irreducible characters of pʹ-degree of G and the irreducible characters of pʹ-degree of NG(P), which preserves field of values of correspondent characters (over the p-adics). This strengthening of the McKay conjecture has several consequences. In this paper we prove one of these consequences: If p 2, then G has no non-trivial pʹ-degree p-rational irreducible characters if and only if NG(P) = P.

Original languageEnglish (US)
Pages (from-to)84-94
Number of pages11
JournalRepresentation Theory
Volume11
Issue number4
DOIs
StatePublished - Apr 19 2007

ASJC Scopus subject areas

  • Mathematics (miscellaneous)

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