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Let      X n {X^n}       denote the smash product of      n n       copies of      R P 2 \mathbb {R}{\mathbb {P}^2}      . We describe a minimal set of generators for      H ∗  ( X n ; Z 2 ) {H^{\ast }}({X^n};{\mathbb {Z}_2})       as a module over the      mod 2 \bmod \,2       Steenrod algebra. The description includes a procedure to obtain all of the generators, a generating function to enumerate them, and a proof of a nice conjecture about how many there are in each dimension.

𝐴₂-annihilated elements in 𝐻_{*}(ΩΣ𝑅𝑃²)