On defect groups for generalized blocks of the symmetric group

In a paper of 2003, Kulshammer, Olsson and Robinson defined l-blocks for the symmetric groups, where l > 1 is an arbitrary integer. In this paper, we give a definition for the defect group of the principal l-block. We then check that, in the Abelian case, we have an analogue of one of Broue's conjectures.