## 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.

### MSC:

 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

Zbl 0904.20016
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