×

\(G\)-identities and \(G\)-varieties. (English. Russian original) Zbl 0966.20014

Algebra Logika 39, No. 3, 249-272 (2000); translation in Algebra Logic 39, No. 3, 141-154 (2000).
G. Baumslag, A. G. Myasnikov, and V. N. Remeslennikov [J. Algebra 219, No. 1, 16-79 (1999; Zbl 0938.20020)] introduced the categories of \(G\)-groups, \(G\)-varieties, \(G\)-identities, and \(G\)-morphisms for an arbitrary group \(G\). The article under review continues this work. Some new theorems in the theory of \(G\)-groups are proven.

MSC:

20E10 Quasivarieties and varieties of groups
14A22 Noncommutative algebraic geometry
20E05 Free nonabelian groups
20E06 Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations
20E34 General structure theorems for groups
20F65 Geometric group theory
20J15 Category of groups

Citations:

Zbl 0938.20020
PDF BibTeX XML Cite
Full Text: EuDML