Geodesic
Reduction theorems for the Brauer conjecture on the number of characters in a $p$-block
Sbornik. Mathematics, Tome 71 (1992) no. 1, pp. 259-269 
P. G. Gres'. Reduction theorems for the Brauer conjecture on the number of characters in a $p$-block. Sbornik. Mathematics, Tome 71 (1992) no. 1, pp. 259-269. http://geodesic.mathdoc.fr/item/SM_1992_71_1_a15/
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Voir la notice de l'article provenant de la source Math-Net.Ru

Theorems are proved that reduce the proof of the Brauer conjecture for finite groups $G$ with a $p$-soluble centralizer of a $p$-element to the evaluation of the minimum of a suitable positive definite quadratic form, whose matrix is given in terms of the Cartan matrix of a $p$-block of a group of simpler structure than $G$.

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