Characters of relative p ' -degree over normal subgroups

• Autores: Gabriel Navarro Ortega , Pham Huu Tiep
• Localización: Annals of mathematics, ISSN 0003-486X, Vol. 178, Nº 3, 2013, págs. 1135-1171
• Idioma: inglés
• DOI: 10.4007/annals.2013.178.3.7
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• Resumen

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