A(p) generators for H*V and Singer's homological transfer

We list explicitly a minimal set of generators for the cohomology of an ele mentary abelian p-group, V, of rank 1 or 2, as a module over the mod p Stee nrod algebra, for an odd prime p. Following Singer, we then construct a tra nsfer map to the vector space spanned by such generators, where V now has a rbitrary 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 iso morphism for V having rank 1 or 2.