Strong amenability and the infinite conjugacy class property

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.Comment: 20 pages, 3 figures. Some minor corrections to the proof