Abstract

Our investigation starts from the question: is the even dimensional cohomology of the non-abelian group of order p 3 and exponent p generated by Chern classes? From the computation of the complete cohomology ring in [8] one quickly sees that the essential problem is to express elements of the form cor ( γ k ), γ ∈ H 2 ( k , ℤ), K a subgroup of index p , in terms of Chern classes. For a more general pair of groups ( K ≤ G ) it is known, see [7] that the best for which one can hope is a description of some multiple of cor ( γ k ) in this way. Our first theorem shows that, under suitable hypotheses (satisfied in particular by the example of order p 3 ) the numerical factor may be removed. Thus

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