In this paper we want to apply the notion of product between ultrafilters to
answer several questions which arise around the Connes' embedding problem. For
instance, we will give a simplification and generalization of a theorem by
Radulescu; we will prove that ultraproduct of hyperlinear groups is still
hyperlinear and consequently the von Neumann algebra of the free group with
uncountable many generators is embeddable into $R^{\omega}$. This follows also
from a general construction that allows, starting from an hyperlinear group, to
find a family of hyperlinear groups.