On topological properties of the formal power series substitution group

Certain topological properties of the group $\text{J}(\text{k})$ of all formal one-variable power series with coefficients in a topological unitary ring $\text{k}$ are considered. We show, in particular, that in the case when $\text{k}=\text{Q}$ the group $\text{J}(\text{Q})$ has no continuous bijections into a locally compact group. In the case when $\text{k}=\mathbb{Z}$ supplied with discrete topology, in spite of the fact that the group $\text{J}(\mathbb{Z})$ 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 $\text{J}(\mathbb{Z})$.