Abelian-by-Cyclic Moufang Loops

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 Rajah , A. ( 2001 ). Moufang loops of odd order pq ³ . J. Algebra 235 ( 1 ): 66 – 93 .Crossref], Web of Science ®] , Google Scholar]] 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.