Residually finite group

In the mathematical field of group theory, a group "G" is residually finite or finitely approximable if for every element "g" that is not the identity in "G" there is a homomorphism "h" from "G" to a finite group, such that 
There are a number of equivalent definitions:
Examples.
Examples of groups that are residually finite are finite groups, free groups, finitely generated nilpotent groups, polycyclic-by-finite groups, finitely generated linear groups, and fundamental groups of compact 3-manifolds.
Subgroups of residually finite groups are residually finite, and direct products of residually finite groups are residually finite. Any inverse limit of residually finite groups is residually finite. In particular, all profinite groups are residually finite.
Examples of non-residually finite groups can be constructed using the fact that all finitely generated residually finite groups are Hopfian groups. For example the Baumslag–Solitar group "B"(2,3) is not Hopfian, and therefore not residually finite.
Profinite topology.
Every group "G" may be made into a topological group by taking as a basis of open neighbourhoods of the identity, the collection of all normal subgroups of finite index in "G". The resulting topology is called the profinite topology on "G". A group is residually finite if, and only if, its profinite topology is Hausdorff.
A group whose cyclic subgroups are closed in the profinite topology is said to be formula_2.
Groups, each of whose finitely generated subgroups are closed in the profinite topology are called subgroup separable (also LERF, for "locally extended residually finite").
A group in which every conjugacy class is closed in the profinite topology is called conjugacy separable.
Varieties of residually finite groups.
One question is: what are the properties of a variety all of whose groups are residually finite? Two results about these are: