Varieties of algebras that are solvable of index 2

Let $\mathfrak M$ be one of the varieties $\operatorname{Alt}_2$, $(-1,1)_2$, $\operatorname{Malc}_2$ or $\operatorname{Jord}_2$ and let $\mathscr M$ be the set of all non-nilpotent subvarieties of $\mathfrak M$. This set is provided in a natural way with a certain topology. A characterization of $\mathfrak M$ is given in terms of the corresponding structure on $\mathscr M$.
Bibliography: 12 titles.