Compressible subgroups and simplicity
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866915080790081536 |
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| author | Garrido, Alejandra Reid, Colin D. |
| author_facet | Garrido, Alejandra Reid, Colin D. |
| contents | In this article we give sufficient conditions for a group to have simple derived subgroup; the argument is based on generalising properties observed for extremely proximal micro-supported actions on the Cantor space, and generalises previous results of Matui, Le Boudec and others in this direction. We give a sufficient condition for a non-trivial normal subgroup (not assumed closed) of a locally compact group $G$ to be open, also based on the theory of micro-supported actions. This shows in particular that many of the class of robustly monolithic groups introduced by Caprace--Reid--Wesolek are simple-by-discrete. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_18891 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Compressible subgroups and simplicity Garrido, Alejandra Reid, Colin D. Group Theory 20E32, 22F50, 22D05, 20E08, 37B05 In this article we give sufficient conditions for a group to have simple derived subgroup; the argument is based on generalising properties observed for extremely proximal micro-supported actions on the Cantor space, and generalises previous results of Matui, Le Boudec and others in this direction. We give a sufficient condition for a non-trivial normal subgroup (not assumed closed) of a locally compact group $G$ to be open, also based on the theory of micro-supported actions. This shows in particular that many of the class of robustly monolithic groups introduced by Caprace--Reid--Wesolek are simple-by-discrete. |
| title | Compressible subgroups and simplicity |
| topic | Group Theory 20E32, 22F50, 22D05, 20E08, 37B05 |
| url | https://arxiv.org/abs/2412.18891 |