The main goal of this joint work is to obtain information about the structure of H-spaces by means of the localization and cellularization functors with respect to Eilenberg-MacLane spaces K(Z/pZ,n). The case n=1 was considered and described by J.A. Crespo in his thesis. 

   The localization and cellularization techniques allow us to somehow generalize the situation for n>1.  Let X be an H-space, the main result is that under some finiteness conditions (assume \Omega^k X is K(Z/pZ,n)-local for some k\geq 0), the fibre of the nullification map with respect to K(Z/pZ,n) is a p-torsion Postnikov piece with bounded homotopy. 

   This result allow us to obtain explicit computations of  the cellularization of H-spaces with respect to Eilenberg-MacLane spaces.