Brauer relations for finite groups in the ring of semisimplified modular representations

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 Fp[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.