Abelian-by-Cyclic Moufang Loops

Abstract

We use groups with triality to construct a series of nonassociative Moufang loops. Certain members of this series contain an abelian normal subloop with the corresponding quotient being a cyclic group. In particular, we give a new series of examples of finite abelian-by-cyclic Moufang loops. The previously known [10] loops of this type of odd order 3q 3, with prime q ≡ 1 (mod 3), are particular cases of our series. Some of the examples are shown to be embeddable into a Cayley algebra.