Group metrics for graph products of cyclic groups

Gianluca Paolini*, Saharon Shelah

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

We complement the characterization of the graph products of cyclic groups G(Γ,p) admitting a Polish group topology of [9] with the following result. Let G=G(Γ,p), then the following are equivalent: (i) there is a metric on Γ which induces a separable topology in which EΓ is closed;(ii) G(Γ,p) is embeddable into a Polish group;(iii) G(Γ,p) is embeddable into a non-Archimedean Polish group.We also construct left-invariant separable group ultrametrics for G=G(Γ,p) and Γ a closed graph on the Baire space, which is of independent interest.

Original languageEnglish
Pages (from-to)281-287
Number of pages7
JournalTopology and its Applications
Volume232
DOIs
StatePublished - 1 Dec 2017

Bibliographical note

Publisher Copyright:
© 2017 Elsevier B.V.

Keywords

  • Combinatorial group theory
  • Descriptive set theory
  • Graph products of groups
  • Polish group topologies

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