English

Quotients by countable subgroups are hyperfinite

Group Theory 2020-02-24 v2 Dynamical Systems Logic

Abstract

We show that for any Polish group GG and any countable normal subgroup ΓG\Gamma\triangleleft G, the coset equivalence relation G/ΓG/\Gamma is a hyperfinite Borel equivalence relation. In particular, the outer automorphism group of any countable group is hyperfinite.

Keywords

Cite

@article{arxiv.1909.08716,
  title  = {Quotients by countable subgroups are hyperfinite},
  author = {Joshua Frisch and Forte Shinko},
  journal= {arXiv preprint arXiv:1909.08716},
  year   = {2020}
}

Comments

7 pages; corrected implication (discrete -> smooth)

R2 v1 2026-06-23T11:19:43.768Z