Minimally nonassociative nilpotent Moufang loops

This paper considers the following question: “Which varieties of Moufang loops have the property that the minimally nonassociative loops in the variety are precisely those which are indecomposable and which can be generated by three elements?” It was shown previously [O. Chein, E.G. Goodaire, Results Math. 39 (2001) 11–17] that the variety of commutative Moufang loops has this property. Here we investigate the variety of centrally nilpotent Moufang loops. We find that while this variety as a whole does not have the property in question, the subvariety consisting of Moufang loops which are centrally nilpotent of class 2 does. We also find some other families of loops which have this property, and consider a number of examples.