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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 $ 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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Additional Information

Ramón J. Flores
Affiliation: Departamento de Matemáticas, Universidad Autónoma de Barcelona, E–08193 Bellaterra, Spain
Email: ramonj@mat.uab.es

DOI: https://doi.org/10.1090/S0002-9947-06-03926-2
Keywords: (Co)localization, finite groups, Eilenberg-MacLane spaces.
Received by editor(s): January 27, 2005
Published electronically: October 17, 2006
Additional Notes: This work was partially supported by MCYT grant BFM2001-2035.
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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