  Certain topological properties of the group $\J(\k)$ of all formal
one-variable power series with coefficients in a topological unitary ring $\k$
are considered. We show, in particular, that in the case when $\k=\Q$ the group
$\J(\Q)$ has no continuous bijections into a locally compact group. In the case
when $\k=\Z$ supplied with discrete topology, in spite of the fact that the
group $\J(\Z)$ has continuous bijections into compact groups, it cannot be
embedded into a locally compact group. In the final part of the paper the
compression property for topological groups is considered. We establish the
compressibility of $\J(\Z)$.
