English

A non-uniformly inner amenable group

Group Theory 2023-12-05 v3 Logic Operator Algebras

Abstract

We provide an example of two elementarily equivalent countable ICC groups GG and HH such that GG is amenable and HH is not inner amenable. As a result, we provide the first example of elementarily equivalent groups whose group von Neumann algebras are not elementarily equivalent, answering a question asked by many researchers.

Keywords

Cite

@article{arxiv.2311.15409,
  title  = {A non-uniformly inner amenable group},
  author = {Isaac Goldbring},
  journal= {arXiv preprint arXiv:2311.15409},
  year   = {2023}
}

Comments

8 pages; third version; Question 4.6 in second version answered affirmatively; comments welcome!

R2 v1 2026-06-28T13:31:59.248Z