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\(G\)-identities of nilpotent groups. I. (English. Russian original) Zbl 0979.20029
Algebra Logika 40, No. 1, 3-21 (2001); translation in Algebra Logic 40, No. 1, 1-11 (2001).
M. G. Amaglobeli and V. N. Remeslennikov [Algebra Logika 39, No. 3, 249-272 (2000; Zbl 0966.20014)] and G. Baumslag, A. Myasnikov, and V. Remeslennikov [J. Algebra 219, No. 1, 16-79 (1999; Zbl 0938.20020)] developed algebraic geometry over groups. In the article under review, the author finds the structure of \(G\)-varieties in case \(G\) is a nilpotent group of class at most 2.

20E10 Quasivarieties and varieties of groups
14A22 Noncommutative algebraic geometry
20F18 Nilpotent groups
20E34 General structure theorems for groups
20F65 Geometric group theory
20J15 Category of groups
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