The Generalized Smith Indices. I.
We are interested in a topological realization of a family of pseudoreflection groups ; i.e. we are looking for topological spaces whose mod-p cohomology is isomorphic to the ring of invariants . Spaces of this type give partial answers to a problem of Steenrod, namely which polynomial algebras over can appear as the mod-p cohomology of a space. The family under consideration is given by pseudoreflection groups which are subgroups of the wreath product where q divides p - 1 and where p is...
It is shown that the classification of polynomial algebras over the mod p Steenrod algebra is an essentially different problem from the classification of polynomial algebras truncated at height greater than p over the Steenrod algebra.