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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.

MSC:
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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