Nullification and cellularization of classifying spaces of finite groups

Abstract

In this note we discuss the effect of the BZ/p-nullification PBZ/p and the BZ/p-cellularization CWBZ/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 PBZ/pBG 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 PBZ/pBG and CWBZ/pBG.