2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/152992For a CSA group $G$ and a wide class of abelian groups $A$ we give an explicit construction for the tensor $A$-completion of $G$ using free products with amalgamations. We apply the obtained results to the study of basic properties of $A$-free groups. In particular, canonical and reduced forms of elements in $A$-free groups are introduced, and then commuting and conjugate elements are described.LaTex, 33 pages, no figures. Submitted to Intern. J. Alg. CompGroup Theorytext