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Right Bol loops are loops satisfying the identity ((zx)y)x=z((xy)x), and right Bruck loops are right Bol loops satisfying the identity (xy)−1=x−1y−1. Let p and q be odd primes such that p>q. Advancing the research program of Niederreiter and Robinson from 1981, we classify right Bol loops of order pq. When q does not divide p2−1, the only right Bol loop of order pq is the cyclic group of order...
In 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...
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