Postnikov Pieces and Bℤ/p-Homotopy Theory

We present a constructive method to compute the cellularization with respect to $B^{m}ℤ/p$ for any integer m ≥ 1 of a large class of H-spaces, namely all those which have a finite number of non-trivial $B^{m}ℤ/p$ -homotopy groups (the pointed mapping space $\text{map}_{\ast}(B^{m}ℤ/p,X)$ is a Postnikov piece). We prove in particular that the $B^{m}ℤ/p$ -cellularization of an H-space having a finite number of $B^{m}ℤ/p$ -homotopy groups is a p-torsion Postnikov piece. Along the way, we characterize the $Bℤ/p^{r}$ -cellular classifying spaces of nilpotent groups.