\mathcal{A}(p) generators for H^*V and Singer's homological transfer

We list explicitly a minimal set of generators for the cohomology of an elementary abelian p-group, V, of rank 1 or 2, as a module over the mod p Steenrod algebra, for an odd prime p. Following Singer, we then construct a transfer map to the vector space spanned by such generators, where V now has arbitrary rank, from the homology of the Steenrod algebra. We show that this map takes images in the subspace of GL(V)-invariants and that it is an isomorphism for V having rank 1 or 2. Received June 11, 1996; in final form June 9, 1997