2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/65443Gromov constructed uncountably many pairwise non-isomorphic discrete groups with Kazhdan's property (T). We will show that no separable II_1-factor can contain all these groups in its unitary group. In particular, no separable II_1-factor can contain all separable II_1-factors in it. We also show that the full group C*-algebras of some of these groups fail the lifting property.4 pages. Largely revised to include an account for the construction of uncountably many simple T groupsOperator Algebras46L10; 20F65text