Symmetric groups, wreath products, Morita equivalences,
and Brou\'e's abelian defect group conjecture 
Joseph Chuang and Radha Kessar

Abstract. 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 $S_p \wreath S_w$. Combined with work of
J. Rickard, this proves that Brou\'e's abelian defect
group conjecture holds for $p$-blocks of symmetric
groups of defect at most $5$.