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In this note we discuss the effect of the BZ/p-nullification P BZ/P and the BZ/p-cellularization CW Bz/p over classifying spaces of finite groups, and we relate them with the corresponding functors with respect to Moore spaces that have been intensively studied in the last years. We describe P BZ/p BG by means of a covering fibration, and we classify all finite groups G for which BG is BZ/p-cellular. We also carefully study the analogous functors in the category of groups, and their relationship with the fundamental groups of P BZ/p BG and CW BZ/p BG.

Nullification and cellularization of classifying spaces of finite groups