### Abstract

We present a constructive method to compute the cellularization with respect to Bmℤ/p for any integer m ≥ 1 of a large class of H-spaces, namely all those which have a finite number of non-trivial Bmℤ/p-homotopy groups (the pointed mapping space map*(Bmℤ/p,X) is a Postnikov piece). We prove in particular that the Bmℤ/p- cellularization of an H-space having a finite number of Bmℤ/p- homotopy groups is a p-torsion Postnikov piece. Along the way, we characterize the Bℤ/pr-cellular classifying spaces of nilpotent groups. © 2006 American Mathematical Society.

Original language | English |
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Pages (from-to) | 1099-1113 |

Journal | Transactions of the American Mathematical Society |

Volume | 359 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1 Mar 2007 |

### Keywords

- Cellularization
- H-spaces
- Nilpotent groups.
- Postnikov pieces

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## Cite this

Castellana, N., Crespo, J. A., & Scherer, J. (2007). Postnikov pieces and Bℤ/p-homotopy theory.

*Transactions of the American Mathematical Society*,*359*(3), 1099-1113. https://doi.org/10.1090/S0002-9947-06-03957-2