2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/69735To solve two problems of Bergman stated in 1981, we construct a group $G$ such that $G$ contains a free noncyclic subgroup (hence, $G$ satisfies no group identity) and $G$, as a group, is generated by its subsemigroup that satisfies a nontrivial semigroup identity.7 pagesGroup Theory20E10, 20F05, 20F06, 20M05text