Property FW and wreath products of groups: a simple approach using Schreier graphs

Abstract

The group property FW stands in-between the celebrated Kazdhan's property (T) and Serre's property FA. Among many characterizations, it might be defined using the number of ends of Schreier graphs. Using this, we show that a finitely generated wreath product $G\wr_XH$ has property FW if and only if both $G$ and $H$ have property FW and $X$ is finite.Comment: v2: corrected the proof of lemma 2.5; results are unchanged. 10 pages, 5 figures. Comments are welcom