On the subalgebra of image annihilated by Steenrod operations Original Research Article

We define a homomorphism θ on image having the property that it is zero on elements hit by the positive degree elements of the Steenrod algebra. We describe the subalgebra (Im θ)* of Steenrod-annihilated elements of image and in particular we show that it is nilpotent of order n + 1. We make some conjectures as to properties of image including a nilpotency conjecture that is a strengthening of the conjecture of Peterson, proved by Wood, concerning the degrees containing elements not hit by positive degree Steenrod operations.