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

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

Paul-Henry Leemann
, Grégoire Schneeberger^*

^*Corresponding author for this work

Department of Pure Mathematics

University of Geneva

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

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 ≀_X H 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.

Original language	English
Pages (from-to)	1261-1270
Number of pages	10
Journal	Expositiones Mathematicae
Volume	40
Issue number	4
DOIs	https://doi.org/10.1016/j.exmath.2022.07.001
Publication status	Published - Dec 2022

Keywords

Wreath products
Property FW
Schreier graphs
Ends

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10.1016/j.exmath.2022.07.001Licence: CC BY

Wreath products of groups acting with bounded orbits
Leemann, P.-H., 12 Mar 2024, In: Enseignement mathématiques. 70, 1/2, p. 121-149
Research output: Contribution to journal › Article › peer-review

Open Access

Cite this

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abstract = "The group property FW stands in-between the celebrated Kazhdan{\textquoteright}s property (T) and Serre{\textquoteright}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 ≀\_X H 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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AB - 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 ≀_X H 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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KW - Schreier graphs

KW - Ends

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JO - Expositiones Mathematicae

JF - Expositiones Mathematicae

IS - 4

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

Abstract

Keywords

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Research output

Wreath products of groups acting with bounded orbits

Cite this