  We investigate the property of elimination of imaginaries for some special
cases of ordered abelian groups. We show that certain Hahn products of ordered
abelian groups do not eliminate imaginaries in the pure language of ordered
groups. Moreover, we prove that, adding finitely many constants to the language
of ordered abelian groups, the theories of the finite lexicographic products
$\mathbb{Z}^n$ and $\mathbb{Z}^n \times \mathbb{Q}$ have definable Skolem
functions.
