JournalslemVol. 59, No. 3/4pp. 271–286

On topological properties of the formal power series substitution group

  • I. Babenko

    Université Montpellier II, France
  • S. Bogatyi

    Moscow State University (Lomonosov), Russian Federation
On topological properties of the formal power series substitution group cover
Download PDF

Abstract

Certain topological properties of the group J(k)\mathcal J(\bf k) of formal one-variable power series with coefficients in a commutative topological unitary ring k\bf k are considered. We show, in particular, that in the case of k=Z\bf k=\mathbb Z equipped with the discrete topology, in spite of the fact that the group J(Z)\mathcal J(\mathbb Z) has continuous monomorphisms into compact groups, it cannot be embedded into a locally compact group. In the case where k=Q\bf k=\mathbb Q the group J(Q)\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 J(k)\mathcal J(\bf k) for a number of rings, in particular for the group J(Z)\mathcal J(\mathbb Z).

Cite this article

I. Babenko, S. Bogatyi, On topological properties of the formal power series substitution group. Enseign. Math. 59 (2013), no. 3/4, pp. 271–286

DOI 10.4171/LEM/59-3-3