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The E2-term of the 2-local EHP spectral sequence is shown to be a Z/2 module. 4 is the order of the identity map on the double loop space of the fiber W(n) of the double suspension E2: S2"'1 -» fi252"+1 .doi:10.2307/2160728 fatcat:5xosf7oc2bgwvb5uaiuavz7o6i