Finite-rank free metabelian subgroups of finitely presented metabelian groups

A sufficient condition is obtained for the residual torsion-free nilpotence of certain finitely presented metabelian groups that arise from a matrix representation developed by Magnus (1939, Ann. of Math. 40, 764-768) for metabelian groups. Using this condition and a construction due to Baumslag (1973, J. Austral. Math. Soc. 16, 98-110), we prove that a free metabelian group of finite rank can be embedded in a finitely presented metabelian group that is also residually torsion-free nilpotent. (C) 1996 Academic Press, Inc.