  In this short note we investigate some consequences of the vanishing of
simple biset functors. As corollary, if there is no non-trivial vanishing of
simple biset functors (e.g. if the group is commutative), then we show that the
double Burnside algebra is a quasi-hereditary algebra in characteristic zero.
In general, this not true without the non-vanishing condition, as over a field
of characteristic zero, the double Burnside algebra of the alternating group of
degree 5 has infinite global dimension.
