CO-H-STRUCTURES ON MOORE SPACES OF TYPE (G,2)

We consider the set (of homotopy classes) of Co-H-structures on a Moor e space M(G, n), where G is an abelian group and n is an integer great er-than-or-equal-to 2. It is shown that for n > 2 the set has one elem ent and for n = 2 the set is in one-one correspondence with Ext(G, G X G). We make a detailed investigation of the co-H-structures on M(G, 2 ) in the case G = Z(m), the integers mod m. We give a specific indexin g of the co-H-structures on M(Z(m), 2) and of the homotopy classes of maps from M(Z(m), 2) to M(Z(n), 2) by means of certain standard homoto py elements. In terms of this indexing we completely determine the co- H-maps from M(Z(m), 2) to M(Z(n), 2) for each co-H-structure on M(Z(m) , 2) and on M(Z(n), 2). This enables us to describe the action of the group of homotopy equivalences of M(Z(m), 2) on the set of co-H-struct ures of M(Z(m), 2). We prove that the action is transitive. From this it follows that if m is odd, all co-H-structures on M(Z(m), 2) are ass ociative and commutative, and if m is even, all co-H-structures on M(Z (m), 2) are associative and non-commutative.