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We show (among other things) that Brauer's k(B)-conjecture holds for defectgroups with are central extensions of metacyclic 2-groups by cyclic groups. Thesame holds for defect groups which contain a central cyclic subgroup of indexat most 9. In particular the k(B)-conjecture holds for 2-blocks of defect atmost 4 and 3-blocks of defect at most 3. As a byproduct we obtain the blockinvariants of 2-blocks with minimal nonmetacyclic defect groups.

Cartan matrices and Brauer's k(B)-conjecture