Nullification and cellularization of classifying spaces of finite groups

Flores, Ramón

doi:10.1090/S0002-9947-06-03926-2

Nullification and cellularization of classifying spaces of finite groups

Author: Ramón J. Flores
Journal: Trans. Amer. Math. Soc. 359 (2007), 1791-1816
MSC (2000): Primary 55P20, 55P60
DOI: https://doi.org/10.1090/S0002-9947-06-03926-2
Published electronically: October 17, 2006
MathSciNet review: 2272149
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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 $\mathbf{CW}_{\textrm{B}\mathbb{Z}/p}\textrm{B}G.$

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