Nullification and cellularization of classifying spaces of finite groups
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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 $\mathbf {CW}_{\textrm {B}\mathbb {Z}/p}\textrm {B}G.$References
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Additional Information
- Ramón J. Flores
- Affiliation: Departamento de Matemáticas, Universidad Autónoma de Barcelona, E–08193 Bellaterra, Spain
- ORCID: 0000-0002-4315-9957
- Email: ramonj@mat.uab.es
- Received by editor(s): January 27, 2005
- Published electronically: October 17, 2006
- Additional Notes: This work was partially supported by MCYT grant BFM2001-2035.
- © Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 2272149