  We provide a necessary and sufficient condition for the embeddability of a
metrizable group into semigroup compactifications associated to uniformly
continuous functions. Our result employs a technique used by I. Ben Yaacov, A.
Berenstein and S. Ferri, and generalizes a theorem by them. This paper is part
of the author's Ph.D. dissertation written under the supervision of Stefano
Ferri and Jorge Galindo at Universidad de los Andes (Bogot\'a-Colombia).
