Characters of relative p'-degree over normal subgroups

Gabriel Navarro, Pham Huu Tiep

Research output: Contribution to journalArticle

27 Scopus citations

Abstract

Let Z be a normal subgroup of a nite group G, let λ ε Irr(Z) be an irreducible complex character of Z, and let p be a prime number. If p does not divide the integers x(1)/λ(1) for all x ε Irr(G) lying over λ then we prove that the Sylow p-subgroups of G=Z are abelian. This theorem, which generalizes the Gluck-Wolf Theorem to arbitrary nite groups, is one of the principal obstacles to proving the celebrated Brauer Height Zero Conjecture.

Original languageEnglish (US)
Pages (from-to)1135-1171
Number of pages37
JournalAnnals of Mathematics
Volume178
Issue number3
DOIs
StatePublished - Sep 24 2013

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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