THE SUBRING OF GROUP COHOMOLOGY CONSTRUCTED BY PERMUTATION REPRESENTATIONS

Each permutation representation of a finite group $G$ can be used to pull cohomology classes back from a symmetric group to $G$. We study the ring generated by all classes that arise in this fashion, describing its variety in terms of the subgroup structure of $G$.We also investigate the effect of restricting to special types of permutation representations, such as $\mathrm{GL}_n(\mathbb{F}_p)$ acting on flags of subspaces.AMS 2000 Mathematics subject classification: Primary 20J06