Cartan invariants and central ideals of group algebras

In this paper we investigate general properties of Cartan invariants of a finite group G in characteristic 2. One of our results shows that the Cartan matrix of G in characteristic 2 contains an odd diagonal entry if and only if G contains a real element of 2-defect zero. We also apply these results to 2-blocks of symmetric groups and to blocks with normal or abelian defect groups. The second part of the paper deals with annihilators of certain ideals in centers of group algebras and blocks.