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MR719669 (86g:55007) 55P35 (18F25 19L64 55P47 55Q05 55Q25 55S15)
Caruso, J.; Cohen, F. R.; May, J. P.; Taylor, L. R. James maps, Segal maps, and the Kahn-Priddy theorem. Trans. Amer. Math. Soc. 281 (1984), no. 1, 243–283.
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