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This response is to the question raised above whether S^7_(2), the 2-localization of the 7-sphere, can admit a homotopy associative multiplication. The answer is no. This fact was established by I.M. James. A later proof by Daciberg Goncalves, "Mod 2 homotopy associative H-spaces" in Geometric Applications of Homotopy Theory I 198-216, Edited by M.G.Barratt and M.E. Mahowald, Lecture Notes in Mathematics 657, Springer-Verlag (1978), revealed the universal nature of the obstruction. The proof involves a secondary cohomology operation and has wider implications. In the same volume, John Hubbock gave a K-theory proof. The calculation of the secondary operation is also presented in the book "Secondary Cohomology Operations" Graduate Studies in Mathematics 49 AMS, by the undersigned. The details are on pages 192-3, and 217-8.