Abstract
The structure of the set of all nonnilpotent subvarieties of the variety of two-step solvable algebras of type (γ, δ) is studied. An additive basis of a free metabelian (γ, δ)-algebra is constructed. It is proved that any identity in a nonnilpotent metabelian (γ, δ)-algebra of degree at least 6 is a consequence of four defining relations.
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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 10, No. 3, pp. 157–180, 2004.
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Platonova, S.V. Varieties of two-step solvable algebras of type (γ, δ). J Math Sci 139, 6762–6779 (2006). https://doi.org/10.1007/s10958-006-0389-y
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DOI: https://doi.org/10.1007/s10958-006-0389-y