  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.
