### Abstract

n this paper, we investigate Moufang p-loops of nilpotency class at least three for p>3. The smallest examples have order p5 and satisfy the following properties: (1) They are of maximal nilpotency class, (2) their associators lie in the center, and (3) they can be constructed using a general form of the semidirect product of a cyclic group and a group of maximal class. We present some results concerning loops with these properties. As an application, we classify proper Moufang loops of order p^5, p>3, and collect information on their multiplication groups.

Lingua originale | English |
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pagine (da-a) | 547-564 |

Numero di pagine | 18 |

Rivista | Journal of Algebra |

Volume | 307, Issue 2 |

Stato di pubblicazione | Published - 2007 |

Pubblicato esternamente | Yes |

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## Cita questo

Valsecchi, M. (2007). On nilpotent Moufang loops with central associators.

*Journal of Algebra*,*307, Issue 2*, 547-564.