2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/100178We present some results about quasiconvex subgroups of infinite index and their products. After that we extend the standard notion of a subgroup commensurator to an arbitrary subset of a group, and generalize some of the previously known results.27 pages, 5 figures. Final version; a number of typos corrected in the replacementGroup Theory2000 MSC: 20F67(primary), 20E45 (secondary)text