2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/143186For a certain class of compact oriented 3-manifolds, M. Goussarov and K. Habiro have conjectured that the information carried by finite-type invariants should be characterized in terms of ``cut-and-paste'' operations defined by the lower central series of the Torelli group of a surface. In this paper, we observe that this is a variation of a classical problem in group theory, namely the ``dimension subgroup problem.'' This viewpoint allows us to prove, by purely algebraic methods, an analogue of the Goussarov-Habiro conjecture for finite-type invariants with values in a fixed field. We deduce that their original conjecture is true at least in a weaker form.20 pages, 7 figures. Minor changes in this final versionGeometric Topology57M27, 16S34text