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.
|Numero di pagine||18|
|Rivista||Journal of Algebra|
|Volume||307, Issue 2|
|Stato di pubblicazione||Published - 2007|