Strong amenability and the infinite conjugacy class property
Group Theory
2020-01-08 v5 Dynamical Systems
Abstract
A group is said to be strongly amenable if each of its proximal topological actions has a fixed point. We show that a finitely generated group is strongly amenable if and only if it is virtually nilpotent. More generally, a countable discrete group is strongly amenable if and only if none of its quotients have the infinite conjugacy class property.
Cite
@article{arxiv.1801.04024,
title = {Strong amenability and the infinite conjugacy class property},
author = {Joshua Frisch and Omer Tamuz and Pooya Vahidi Ferdowsi},
journal= {arXiv preprint arXiv:1801.04024},
year = {2020}
}
Comments
20 pages, 3 figures. Some minor corrections to the proofs