Geodesic
Characters of relative $p’$-degree over normal subgroups
Gabriel Navarro1 ; Pham Huu Tiep2
1 Departament d'Àlgebra, Universitat de València, València, Spain
2 University of Arizona, Tucson, AZ
Annals of mathematics, Tome 178 (2013) no. 3, pp. 1135-1171.

Voir la notice de l'article provenant de la source Annals of Mathematics website

Let $Z$ be a normal subgroup of a finite group $G$, let $\lambda \in \mathrm{Irr}(Z)$ be an irreducible complex character of $Z$, and let $p$ be a prime number. If $p$ does not divide the integers $\chi(1)/\lambda(1)$ for all $\chi \in \mathrm{Irr}(G)$ lying over $\lambda$, 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.
DOI : 10.4007/annals.2013.178.3.7

Gabriel Navarro 1 ; Pham Huu Tiep 2

1 Departament d'Àlgebra, Universitat de València, València, Spain
2 University of Arizona, Tucson, AZ 
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Gabriel Navarro; Pham Huu Tiep. Characters of relative $p’$-degree over normal subgroups. Annals of mathematics, Tome 178 (2013) no. 3, pp. 1135-1171. doi : 10.4007/annals.2013.178.3.7. http://geodesic.mathdoc.fr/articles/10.4007/annals.2013.178.3.7/

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