Published July 2, 2023
| Version Published
Journal Article
Open
Quotients by countable normal subgroups are hyperfinite
Abstract
We show that for any Polish group G and any countable normal subgroup Γ◃G, the coset equivalence relation G/Γ is a hyperfinite Borel equivalence relation. In particular, the outer automorphism group of any countable group is hyperfinite.
Copyright and License
©2023 European Mathematical Society. Published by EMS Press. This work is licensed under a CC BY 4.0 license.
Acknowledgement
We would like to thank Aristotelis Panagiotopoulos for posing the original question about outer automorphisms, and Alexander Kechris, Andrew Marks and Todor Tsankov for many helpful comments.
Funding
The authors were partially supported by NSF Grant DMS-1464475.
Files
10.4171-ggd-719.pdf
Additional details
Related works
- Is new version of
- Discussion Paper: arXiv:1909.08716 (arXiv)
Funding
- National Science Foundation
- DMS-1464475
Dates
- Accepted
-
2022-05-11Accepted
Caltech Custom Metadata
- Publication Status
- Published