On defect groups for generalized blocks of the symmetric group

In a paper of 2003, Külshammer, Olsson and Robinson defined-blocks for the symmetric groups, where >1 is an arbitraryinteger. In this paper, we give a definition for the defectgroup of the principal -block. We then check that, in the Abeliancase, we have an analogue of one of Broué's conjectures.