Geodesic
Varieties of Two-Step Solvable Algebras of Type~(1,1)
Matematičeskie zametki, Tome 76 (2004) no. 3, pp. 409-419

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The structure of the set of all non-nilpotent subvarieties of the variety of two-step solvable algebras of type (1,1) is studied. An additive basis of a free metabelian (1,1)-algebra is constructed. It is proved that any identity in a non-nilpotent metabelian (1,1)-algebra of degree $\geqslant6$ is a consequence of four defining relations. 
@article{MZM_2004_76_3_a9,
     author = {S. V. Platonova},
     title = {Varieties of {Two-Step} {Solvable} {Algebras} of {Type~(1,1)}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {409--419},
     publisher = {mathdoc},
     volume = {76},
     number = {3},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2004_76_3_a9/}
}
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S. V. Platonova. Varieties of Two-Step Solvable Algebras of Type~(1,1). Matematičeskie zametki, Tome 76 (2004) no. 3, pp. 409-419. http://geodesic.mathdoc.fr/item/MZM_2004_76_3_a9/