Search results for "Loops of maximal cla"

On nilpotent Moufang loops with central associators

2007

Abstract In this paper, we investigate Moufang p-loops of nilpotency class at least three for p > 3 . The smallest examples have order p 5 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.