No uncountable Polish group can be a right-angled Artin group

Gianluca Paolini*, Saharon Shelah

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

We prove that if G is a Polish group and A a group admitting a system of generators whose associated length function satisfies: (i) if 0 < k < ω, then lg(x) ≤ lg(xk); (ii) if lg(y) < k < ω and xk = y, then x = e, then there exists a subgroup G* of G of size b (the bounding number) such that G* is not embeddable in A. In particular, we prove that the automorphism group of a countable structure cannot be an uncountable right-angled Artin group. This generalizes analogous results for free and free abelian uncountable groups.

Original languageEnglish
Article number13
JournalAxioms
Volume6
Issue number2
DOIs
StatePublished - 1 Jun 2017

Bibliographical note

Publisher Copyright:
© 2017 by the authors.

Keywords

  • Descriptive set theory
  • Polish group topologies
  • Right-angled Artin groups

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