On nilpotent Moufang loops with central associators

• DOI: 10.1016/j.jalgebra.2006.01.031
• Publication Date: 2006-11-16T02:28:15Z
• Authors: Gábor P. Nagy; Maurizio Valsecchi
• Keywords: Algebra and Number Theory; Loops of maximal class; Moufang loops; Moufang loops; Nilpotent loops; Loops of maximal class; Semidirect product of loops; Nilpotent loops; 0101 mathematics; Semidirect product of loops; 01 natural sciences

AbstractIn 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 p5, p>3, and collect information on their multiplication groups.