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subgroup complexes

Proceedings of the Edinburgh Mathematical Society (1)

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THE SUBRING OF GROUP COHOMOLOGY CONSTRUCTED BY PERMUTATION REPRESENTATIONS
David J. Green, Ian J. Leary, Björn Schuster
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 45 / Issue 1 / February 2002

Published online by Cambridge University Press:

05 February 2002, pp. 241-253
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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