For some years there have been (k-1)-connected irreducible H-spaces, Y_k, with no p-torsion in homology or homotopy.  All p-torsion free H-spaces are products of these spaces and they show up regularly in the literature. Boardman and I have generalized theses spaces and theorems using (k-1) connected H-spaces, Y_k, that have no v_n torsion in homology or homotopy (to be defined).  These spaces seem ripe for exploitation in the environment of chromatic homotopy theory.