On topological properties of the formal power series substitution group

Details On topological properties of the formal power series substitution group On topological properties of the formal power series substitution group

2009-12-09

arxiv.org/abs/0912.1813v1

Mathematics

Group Theory

10 pages

Scientific paper

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 $\J(\Z)$.

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