The subring of group cohomology constructed by permutation representations

Every homomorphism from a finite group G to a symmetric group S gives rise to a homomorphism from the mod-p cohomology of S to that of G. We describe the prime ideal spectrum of the subring of the cohomology of G generated by all such representations. This subring turns out to be amenable to the techniques introduced by two of us in 15. Much of the paper consists of a comparison of the prime ideal spectra for three distinct rings in the case when G is the general linear group GL(n,p) over the field of p elements. These are the whole mod-p cohomology ring, the subring corresponding to all permutation representations (as described above), and the subring corresponding to the permutation actions on partial flags. For n large and even, we show that no two of these rings are F-isomorphic