P-rational characters and self-normalizing sylow p-subgroups

Gabriel Navarro, Pham Huu Tiep, Alexandre Turull

Research output: Contribution to journalArticle

14 Citations (Scopus)

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 p′-degree of G and the irreducible characters of p′-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 p′-degree p-rational irreducible characters if and only if Ne G(P) = P.

Original languageEnglish (US)
Pages (from-to)84-94
Number of pages11
JournalRepresentation Theory
Volume11
DOIs
StatePublished - 2007
Externally publishedYes

Fingerprint

Irreducible Character
Subgroup
Field of Values
Finite P-group
Strengthening
Bijection
Refinement
If and only if
Character

Keywords

  • McKay conjecture
  • P-rational characters
  • Self-normalizing sylow p-subgroups

ASJC Scopus subject areas

  • Mathematics (miscellaneous)

Cite this

P-rational characters and self-normalizing sylow p-subgroups. / Navarro, Gabriel; Tiep, Pham Huu; Turull, Alexandre.

In: Representation Theory, Vol. 11, 2007, p. 84-94.

Research output: Contribution to journalArticle

Navarro, Gabriel ; Tiep, Pham Huu ; Turull, Alexandre. / P-rational characters and self-normalizing sylow p-subgroups. In: Representation Theory. 2007 ; Vol. 11. pp. 84-94.
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