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
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Trans. Amer. Math. Soc. 359 (2007), 1791-1816 Request permission

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 $G$ 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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