  The isomorphism problem for infinite finitely presented groups is probably
the hardest among standard algorithmic problems in group theory. Classes of
groups where it has been completely solved are nilpotent groups, hyperbolic
groups, and limit groups. In this short paper, we address the problem of
isomorphism to particular groups, including free groups. We also address the
algorithmic problem of embedding a finitely presented group in a given limit
group.
