Strong amenability and the infinite conjugacy class property
arXiv:1801.04024 · doi:10.1007/s00222-019-00896-z
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.
20 pages, 3 figures. Some minor corrections to the proofs