  Let $G$ be a finite group and $p$ be a prime. We study the kernel of the map,
between the Burnside ring of $G$ and the Grothendieck ring of
$\mathbb{F}_p[G]$-modules, taking a $G$-set to its associated permutation
module. We are able, for all finite groups, to classify the primitive quotient
of the kernel; that is for each $G$, the kernel modulo elements coming from the
kernel for proper subquotients of $G$. We are able to identify exactly which
groups have non-trivial primitive quotient and we give generators for the
primitive quotient in the soluble case.
