On multiplication of varieties of algebras (Q1902846)

In generalizing the well-known multiplication of varieties of groups, \textit{A. I. Mat'tsev} had introduced [Sib. Mat. Zh. 8, No. 2, 346-365 (1967; Zbl 0228.08007)] the multiplication of classes of algebraic systems. In the general case, the product of varieties of algebras is not a variety. By this reason there naturally arises the problem of finding conditions under which the \(\mathfrak B\)-product [Mal'tsev, loc. cit.] of two subvarieties of a given variety \(\mathfrak B\) could be its subvariety as well. The problem is the subject of our investigation.