11.72 (1990)

Suppose that a variety of groups $\mathfrak{V}$ is non-regular, that is, the free group $F_{n+1}(\mathfrak{V})$ is embeddable in $F_n(\mathfrak{V})$ for some $n$. Is it true that then every countable group in $\mathfrak{V}$ is embeddable in an $n$-generated group in $\mathfrak{V}$?