11.86 (1990)

Does every group $G = \langle x_1, \dots, x_n \mid r_1 = \dots = r_m = 1 \rangle$ possess, in a natural way, a homomorphic image $H = \langle x_1, \dots, x_n \mid s_1 = \dots = s_m = 1 \rangle$
$\qquad$ a) such that $H$ is a torsion-free group?
$\qquad$ b) such that the integral group ring of $H$ is embeddable in a skew field?

If the stronger assertion b) is true, then this will give an explicit method of finding elements $x_{i_1}, \dots, x_{i_{n-m}}$ which generate a free group in $G$. Such elements exist by N. S. Romanovskiĭ’s theorem (Algebra and Logic, 16, no. 1 (1977), 62–67).