In the variety of all groups, A. I. Mal’cev [5] proved in 1949 that the free product of two residually torsion-free nilpotent groups is again residually torsion-free nilpotent. This paper is motivated by the analogous question in the variety of metabelian groups: can we determine whether free metabelian products of residually torsion-free nilpotent metabelian groups are residually torsion-free ...

We define two finite-dimensional complexes on which the group Aut(Fn) acts freely, and study their homotopy groups. The definitions of these complexes were motivated by lowdimensional pseudo-isotopy theory. So not surprisingly, the complexes are related to a number of spaces arising in algebraic K-theory, and to another in low-dimensional topology. The complexes are denoted by Xn and X alg n . ...