Mal'tsev products of varieties, II

Abstract: The Mal'tsev product of two varieties of the same similarity type is not in general a variety, because it can fail to be closed under homomorphic images. In the previous paper we provided a new sufficient condition for such a product to be a variety. In this paper we extend that result by weakening the assumptions regarding the two varieties. We also explore the various special cases of our new result and provide a number of examples of its application.