  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) $\rightarrow$ 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.

Algebraic Topology