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THE SUBRING OF GROUP COHOMOLOGY CONSTRUCTED BY PERMUTATION REPRESENTATIONS

Published online by Cambridge University Press:  05 February 2002

David J. Green ,
Ian J. Leary  and
Björn Schuster
David J. Green
Affiliation:
Department of Mathematics, University of Wuppertal, D-42097 Wuppertal, Germany
Ian J. Leary
Affiliation:
Faculty of Mathematical Studies, University of Southampton, Southampton SO17 1BJ, UK
Björn Schuster
Affiliation:
Department of Mathematics, University of Wuppertal, D-42097 Wuppertal, Germany
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Abstract

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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

Keywords

group cohomologyfinite groupssubgroup complexespermutation representations
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 45 , Issue 1 , February 2002 , pp. 241 - 253
Copyright
Copyright © Edinburgh Mathematical Society 2002