On a basis of the product of varieties of groups

In this paper it is shown that the products $\mathfrak B_4\cdot\mathfrak B_2$ and $\mathfrak B_4\cdot\mathfrak A$ are infinitely based, where $\mathfrak B_4$ and $\mathfrak B_2$ are the Burnside varieties of groups of exponent four and two, and $\mathfrak A$ is the variety of all abelian groups.