Certain properties of realizable modules over the Steenrod algebra (Q1099844)

Let A be the mod p Steenrod algebra. An A module M is said to be realizable if there exists a spectrum X such that \(H^*(X,Z_ p)\cong M\). In the case \(p=2\), \textit{H. R. Margolis} [Bull. Am. Math. Soc. 78, 564-567 (1972; Zbl 0256.55017)] gave a construction for killing the \(P^ s_ t\) homology groups of M in the category of A modules. Since the construction can also be carried out in the category of realizable A modules, if M is realizable then the constructed new module is also realizable; this gives a necessary condition for realizability. In the present paper the author considers the case \(p>2\) and obtains a corresponding result for the element \(P^ 0_ 1\).