Symmetric Groups, Wreath Products, Morita Equivalences, and Broué'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 [rmoust ] S w . Combined with work of J. Rickard, this proves that Broué's abelian defect group conjecture holds for p -blocks of symmetric groups of defect at most 5.