  Let $k$ be a field of characteristic $p > 0$. For $G$ an elementary abelian
$p$-group, there exist collections of permutation module such that if $C^*$ is
any exact bounded complex whose terms are sums of copies of modules from the
collection, then $C^*$ is contractible. A consequence is that if $G$ is any
finite group whose Sylow $p$-subgroups are not cyclic or quaternion, and if
$C^*$ is a bounded exact complex such that each $C^i$ is direct sum of one
dimensional modules and projective modules, then $C^*$ is contractible.
