Certain topological properties of the group
\mathcal J(\bf k)
of formal one-variable power series with coefficients in a commutative topological unitary ring
\bf k
are considered. We show, in particular, that in the case of
\bf k=\mathbb Z
equipped with the discrete topology, in spite of the fact that the group
\mathcal J(\mathbb Z)
has continuous monomorphisms into compact groups, it cannot be embedded into a locally compact group. In the case where
\bf k=\mathbb Q
the group
\mathcal J(\mathbb Q)
has no continuous monomorphisms into a locally compact group. In the last part of the paper the compressibility property for topological groups is considered. This property is valid for
\mathcal J(\bf k)
for a number of rings, in particular for the group
\mathcal J(\mathbb Z)
.
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