On the mod-2 cohomology of some 2-Postnikov towers

The present note presents some results about the mod-2 cohomology, modulo nilpotent elements elements of the fiber E of a decomposable map $\psi$ : K(Z, 2) $\to$ K(Z/2, p). This is more an announcement and a brief description of the tools that are used: Lannes’ T functor and the Eilenberg-Moore spectral sequence.