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Nullification and cellularization of classifying spaces of finite groups

Authors:	Ramó n J Flores

Institution:	Departamento de Matemáticas, Universidad Autónoma de Barcelona, E--08193 Bellaterra, Spain

Abstract:	In this note we discuss the effect of the $\textrm{B}\mathbb{Z}/p$ -nullification $\mathbf{P}_{\textrm{B}\mathbb{Z}/p}$ and the $\textrm{B}\mathbb{Z}/p$ -cellularization $\mathbf{CW}_{\textrm{B}\mathbb{Z}/p}$ 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 $\mathbf{P}_{\textrm{B}\mathbb{Z}/p}\textrm{B}G$ by means of a covering fibration, and we classify all finite groups for which $\textrm{B}G$ is $\textrm{B}\mathbb{Z}/p$ -cellular. We also carefully study the analogous functors in the category of groups, and their relationship with the fundamental groups of $\mathbf{P}_{\textrm{B}\mathbb{Z}/p}\textrm{B}G$ and $\mathbf{CW}_{\textrm{B}\mathbb{Z}/p}\textrm{B}G.$

Keywords:	(Co)localization finite groups Eilenberg-MacLane spaces

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