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POLYNOMIAL INVARIANT RINGS ISOMORPHIC AS MODULES OVER THE STEENROD ALGEBRA

Published online by Cambridge University Press:  13 February 2001

JOEL SEGAL
JOEL SEGAL
Affiliation:
Rote Straße 3, D-37073 Göttingen, Germany; [email protected]
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Abstract

The paper is concerned with rings of polynomial invariants of finite groups. In particular, it will be shown that these rings are isomorphic as modules over the Steenrod algebra [Pscr ]* if and only if the group representations are pointwise conjugate. An application to cohomology is the construction of classifying spaces of finite groups which are not homotopy equivalent, but where the cohomology rings are isomorphic as unstable modules over the (topological) Steenrod algebra.

Type
Research Article
Information
Journal of the London Mathematical Society , Volume 62 , Issue 3 , December 2000 , pp. 729 - 739
Copyright
The London Mathematical Society 2000

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