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

Paul-Henry Leemann; Grégoire Schneeberger

doi:10.1016/j.exmath.2022.07.001

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arXiv · 2101.03817

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

Paul-Henry Leemann·Grégoire Schneeberger

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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, 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 $G\wr_XH$ 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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BibTeX RIS

Paul-Henry Leemann, Grégoire Schneeberger. 2021-01-11. Property FW and wreath products of groups: a simple approach using Schreier graphs. https://doi.org/10.1016/j.exmath.2022.07.001

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