On the property of being finitely based of some solvable varieties of Lie algebras of finite axiomatic rank

In this paper a maximality condition is established for verbal subalgebras of a relatively free algebra, over a field of cardinality at least $c+1$, of the variety $\mathfrak N_c\mathfrak N_d$ of Lie algebras with a finite set of free generators. (The variety $\mathfrak N_c\mathfrak N_d$ consists of the algebras obtained by extending nilpotent Lie algebras of class $c$ by means of nilpotent Lie algebras of class $d$.)
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