Symmetric groups, wreath products, Morita equivalences and Broue's abelian defect group conjecture

It is shown that for any prime p, and any non-negative integer w less than p, there exist p-blocks of symmetric groups of defect w, which are Morita equivalent to the principal p-block of the group S-p graphics S-w. Combined with work of J. Rickard, this proves that Broue's abelian defect group conjecture holds for p-blocks of symmetric groups of defect at most 5.