2-Blocks with minimal nonabelian defect groups

Abstract

We study numerical invariants of 2-blocks with minimal nonabelian defect groups. These groups were classified by R\'edei. If the defect group is also metacyclic, then the block invariants are known. In the remaining cases there are only two (infinite) families of "interesting" defect groups. In all other cases the blocks are nilpotent. We prove Brauer's k(B)-conjecture and the Olsson-conjecture for all 2-blocks with minimal nonabelian defect groups. For one of the two families we also show that Alperin's weight conjecture and Dade's conjecture is satisfied. This paper is a part of the author's PhD thesis.