The subring of group cohomology constructed by permutation representations

Green, David J., Leary, Ian J. and Schuster, Björn (2002) The subring of group cohomology constructed by permutation representations. Proceedings of the Edinburgh Mathematical Society, 45 (1), 241-253.

Record type: Article

Abstract

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.

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