2-Blocks with minimal nonabelian defect groups

We study numerical invariants of 2-blocks with minimal nonabelian defect groups. These groups were classified by Rédei (see Rédei, 1947 [41], ). If the defect group is also metacyclic, then the block invariants are known (see Sambale [43]). In the remaining cases there are only two (infinite) families of ‘interesting’ defect groups. In all other cases the blocks are nilpotent. We prove Brauerʼs k(B)-conjecture and Olssonʼs conjecture for all 2-blocks with minimal nonabelian defect groups. For one of the two families we also show that Alperinʼs weight conjecture and Dadeʼs conjecture are satisfied. This paper is a part of the authorʼs PhD thesis.