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Irreducible affine varieties over a free group. II: Systems in triangular quasi-quadratic form and description of residually free groups. (English) Zbl 0904.20017
This paper completes the programme started in the first paper (see the preceding review Zbl 0904.20016) by proving the theorem: Theorem. A finitely-generated group is fully residually free if and only if it is isomorphic to a subgroup of \(F^{\mathbb{Z}[x]}\). Theorems are also proved which describe the algebraic structure of finitely generated subgroups of \(F^{\mathbb{Z}[x]}\) in terms of free constructions.

20E26 Residual properties and generalizations; residually finite groups
20E05 Free nonabelian groups
20E06 Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations
20F05 Generators, relations, and presentations of groups
20E22 Extensions, wreath products, and other compositions of groups
20E07 Subgroup theorems; subgroup growth
Full Text: DOI
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