Property FW and wreath products of groups: a simple approach using Schreier graphs
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2021
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| _version_ | 1866929281606615040 |
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| author | Leemann, Paul-Henry Schneeberger, Grégoire |
| author_facet | Leemann, Paul-Henry Schneeberger, Grégoire |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2101_03817 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Property FW and wreath products of groups: a simple approach using Schreier graphs Leemann, Paul-Henry Schneeberger, Grégoire Group Theory 20E22 (Primary) 20F65, 05C25 (Secondary) 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. |
| title | Property FW and wreath products of groups: a simple approach using Schreier graphs |
| topic | Group Theory 20E22 (Primary) 20F65, 05C25 (Secondary) |
| url | https://arxiv.org/abs/2101.03817 |