Blocks with defect group D2n×C2m

AbstractWe determine the numerical invariants of blocks with defect group D2n×C2m, where D2n denotes a dihedral group of order 2n and C2m denotes a cyclic group of order 2m. This generalizes Brauer’s results (Brauer, 1974 [2]) for m=0. As a consequence, we prove Brauer’s k(B)-conjecture, Olsson’s conjecture (and more generally Eaton’s conjecture), Brauer’s height zero conjecture, the Alperin–McKay conjecture, Alperin’s weight conjecture and Robinson’s ordinary weight conjecture for these blocks. Moreover, we show that the gluing problem has a unique solution in this case