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Abstract. Let Ps = F2 [xx, ... , xs] be the mod 2 cohomology of the sfold product of RP°° with the usual structure as a module over the Steenrod algebra. A monomial in Ps is said to be hit if it is in the image of the action A Ps -> Ps where A is the augmentation ideal of A . We extend a result of Wood to determine a new family of hit monomials in Ps. We then use similar methods to obtain a generalization of antiautomorphism formulas of Davis and Gallant.

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Abstract.In this paper we prove the existence of global nilpotence and global torsion bounds for the cohomology of any finite Hopf subalgebra of the Steenrod algebra for the prime 2. An explicit formula for computing such bounds is then obtained. This is used to compute bounds for H* (sán ) fer n < 6 .