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13.40 (1995)

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A group $G$ is said to be $\omega$-residually free if, for every finite set of non-trivial elements of $G$, there is a homomorphism of $G$ into a free group such that the images of all these elements are non-trivial. Is every finitely-generated $\omega$-residually free group embeddable in a free $\mathbb{Z}[x]$-group?

Contributor: A. G. Myasnikov, V. N. Remeslennikov

Progress

Yes, it is (O. Kharlampovich, A. Myasnikov, J. Algebra, 200 (1998), 472–570).

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