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Associative h-spaces and algebras

1. Ganea has shown (Theorem 2·2 of (2)) that h-cogroup structures on a CW space coincide, in the homotopy category, with coalgebra structures defined with respect to the cotriple determined by SΩ. The construction used by Ganea to prove this does not dualize. It seems possible moreover that the dual statement is false. In this note I show, using the results of (4), that, for suitable spaces, there is a surjection from the set of algebra structures defined with respect to the triple determined by ΩS to the set of h-group structures, and I construct a right inverse for this surjection.