  For finite groups $G$ with non-abelian, trivial intersection Sylow
$p$-subgroups, the analysis of the Loewy structure of the centre of a block
allows us to deduce that a stable equivalence of Morita type does not induce an
algebra isomorphism between the centre of the principal block of $G$ and the
centre of the Brauer correspondent. This was already known for the Suzuki
groups; the result will be generalised to cover more groups with trivial
intersection Sylow $p$-subgroups.
