8.2 (1982)

Let $G$ be the amalgamated free product of two polycyclic groups, amalgamating a normal subgroup of each. Is $G$ isomorphic to a linear group? $G$ is residually finite (G. Baumslag, Trans. Amer. Math. Soc., 106, no. 2 (1963), 193–209) and the answer is “yes” if the amalgamated part is torsion-free, abelian (B. A. F. Wehrfritz, Proc. London Math. Soc., 27, no. 3 (1973), 402–424) and nilpotent (M. Shirvani, 1981, unpublished).