On the classification of unstable \(H^{\ast}V\)-\(A\)-modules (Q847583)

This paper concerns unstable modules over the Steenrod algebra and addresses the problem of finding all \(H^{*}(V)\)-\(A\) modules \(E\) for which \(\bar{E}\) is isomorphic (as an \(A\)-module) to some given unstable \(A\)-module, where \(\bar{E}\) denotes the space of \(H^{*}(V)\)-generators, i.e., \(\bar{E} = E/\tilde{H}^{*}(V).E\). A solution is given in the cases where \(\bar{E}\) is the Brown-Gitler module \(J(2)\), or is a nil-closed unstable \(A\)-module, or is a suspension of the trivial module \({\mathbb F}_2\).