2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/158068A subset U of a group G is called k-universal if U contains a translate of every k-element subset of G. We give several nearly optimal constructions of small k-universal sets, and use them to resolve an old question of Erdos and Newman on bases for sets of integers, and to obtain several extensions for other groups.12 pagesCombinatoricsGroup TheoryNumber Theory05B10, 11B13, 20D60text