  A finitely generated group $G$ is said to be condensed if its isomorphism
class in the space of finitely generated marked groups has no isolated points.
We prove that every product variety $\mathcal{UV}$, where $\mathcal{U}$
(respectively, $\mathcal{V}$) is a non-abelian (respectively, a
non-locally-finite) variety, contains a condensed group. In particular, there
exist condensed groups of finite exponent. As an application, we obtain some
results on the structure of the isomorphism relation and elementary equivalence
on the set of finitely generated groups in $\mathcal{UV}$.
