Abstract

The group property FW stands in-between the celebrated Kazhdan’s property (T) and Serre’s property FA. Among many characterizations, it might be defined, for finitely generated groups, as having all Schreier graphs one-ended.It follows from the work of Y. Cornulier that a finitely generated wreath product G≀XH has property FW if and only if both G and H have property FW and X is finite. The aim of this paper is to give an elementary, direct and explicit proof of this fact using Schreier graphs.

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