TENSOR COMPLETION FOR A CERTAIN CLASS OF GROUPS

Abstract

In this paper we construct the tensor A-completion over an arbitrary torsion-free ring A for groups whose maximal abelian subgroups are either conjugate separated or A-modules. As a corollary, this result gives us an explicit description of the structure of tensor completion for groups of the form F/N′, in particular, for free solvable groups. We also prove that the class of all A-faithful groups is closed under free products.