2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/126389We show that it is consistent with the axioms of set theory that every infinite profinite group G possesses a closed subset X of Haar measure zero such that less than continuum many translates of X cover G. This answers a question of Elekes and Toth and by their work settles the problem for all infinite compact topological groups.Group TheoryLogictext