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

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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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     author = {P. G. Gres'},
     title = {Reduction theorems for the {Brauer} conjecture on the number of characters in a~$p$-block},
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     url = {http://geodesic.mathdoc.fr/item/SM_1992_71_1_a15/}
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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/