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MR1388199 (97d:55029) 55S10 (16G99 55R40)
Crossley, M. D. ${\scr A}(p)$-annihilated elements in $H\sb *(C{\rm P}\sp \infty\timesC{\rm P}\sp \infty)$. Math. Proc. Cambridge Philos. Soc. 120 (1996), no. 3, 441--453.
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