We define a new invariant for a p-block, the strong Frobenius number, which
we use to address the problem of reducing Donovan's conjecture to normal
subgroups of index p. As an application we use the strong Frobenius number to
complete the proof of Donovan's conjecture for 2-blocks with abelian defect
groups of rank at most 4 and for 2-blocks with abelian defect groups of order
at most 64
