Irreducible Affine Varieties over a Free Group: II. Systems in Triangular Quasi-quadratic Form and Description of Residually Free Groups

@article{Kharlampovich1998IrreducibleAV,
  title={Irreducible Affine Varieties over a Free Group: II. Systems in Triangular Quasi-quadratic Form and Description of Residually Free Groups},
  author={Olga Kharlampovich and Alexei G. Myasnikov},
  journal={Journal of Algebra},
  year={1998},
  volume={200},
  pages={517-570}
}
Abstract We shall prove the conjecture of Myasnikov and Remeslennikov [ 4 ] which states that a finitely generated group is fully residually free (every finite set of nontrivial elements has nontrivial images under some homomorphism into a free group) if and only if it is embeddable in the Lyndon's exponential groupFZ[x], which is theZ[x]-completion of the free group. HereZ[x] is the ring of polynomials of one variable with integer coefficients. Historically, Lyndon's attempts to solve Tarski's… 

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