Cartan Invariants and Central Ideals of Group Algebras
Murray, John and Breuer, Thomas and Hethelyi, Laszlo and Horvath, Erzsebet and Kulshammer, Burkhard (2006) Cartan Invariants and Central Ideals of Group Algebras. Journal of Algebra, 296 . pp. 177-196.
Abstract. 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.
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