Certain unstable modular algebras over the \(\mod p\) Steenrod algebra (Q1279752)

The paper under review gives a further partial answer to the question of which algebras occur as the cohomology of spaces. For \(p\) an odd prime, the author considers algebras with a single polynomial generator and two exterior generators : \({\mathbb Z}/p[x_{2n}] \otimes \Lambda(y_{2n+1}, z_{2n+2p-1})\), with a Bockstein linking \(x\) to \(y\) and a Steenrod power linking \(y\) to \(z\). His first step is to show, using classical techniques, that \(n\) must be a power of \(p\) in order that the specified Steenrod operations be compatible with the algebra structure. Then his second theorem, using Lannes theory, shows that in fact \(n\) must be \(1\), \(p\) or \(p^2\) if the algebra is realizable.