FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2004, VOLUME 10, NUMBER 3, PAGES 157-180

Varieties of two-step solvable algebras of type $($g, d)

S. V. Platonova

Abstract

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The structure of the set of all nonnilpotent subvarieties of the variety of two-step solvable algebras of type $($g, d) is studied. An additive basis of a free metabelian $($g, d)-algebra is constructed. It is proved that any identity in a nonnilpotent metabelian $($g, d)-algebra of degree at least $6$ is a consequence of four defining relations.

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Last modified: February 28, 2005