On defect groups for generalized blocks of the symmetric group
Jean-Baptiste Gramain
March 2007

Abstract. 
In a paper of 2003, B. K\"ulshammer, J. B. Olsson and 
G. R. Robinson defined $\ell$-blocks for the symmetric
groups, where $\ell > 1$ is an arbitrary integer. In
this paper, we give a definition for the defect group
of the principal $\ell$-block. We then check that, in
the Abelian case, we have an analogue of one of
M. Brou\'e's conjectures.