Certain topological properties of the group of formal one-variable power series with coefficients in a commutative topological unitary ring are considered. We show, in particular, that in the case of equipped with the discrete topology, in spite of the fact that the group has continuous monomorphisms into compact groups, it cannot be embedded into a locally compact group. In the case where the group 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 for a number of rings, in particular for the group .
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Ivan Babenko, S. Bogatyi, On topological properties of the formal power series substitution group. Enseign. Math. 59 (2013), no. 3/4, pp. 271–286DOI 10.4171/LEM/59-3-3