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.
Nagy, G., Valsecchi, M. (2007). On nilpotent Moufang loops with central associators. JOURNAL OF ALGEBRA, 307, Issue 2, 547-564.
On nilpotent Moufang loops with central associators
VALSECCHI, Maurizio
2007-01-01
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.