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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2403.16364 |
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| _version_ | 1866914727723008000 |
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| author | Grigorchuk, Rostislav Vorobets, Yaroslav |
| author_facet | Grigorchuk, Rostislav Vorobets, Yaroslav |
| contents | The paper is concerned with maximal subgroups of the ample (better known as topological full) groups of homeomorphisms of totally disconnected compact metrizable topological spaces. We describe all maximal subgroups that are stabilizers of finite sets. Under certain assumptions on the ample group (including minimality), we describe all maximal subgroups that are stabilizers of closed sets or stabilizers of partitions into clopen sets. In particular, our results apply to the ample groups associated with Cantor minimal systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_16364 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On maximal subgroups of ample groups Grigorchuk, Rostislav Vorobets, Yaroslav Group Theory Dynamical Systems 20E28, 20F38, 20F65, 37B02, 37B05 The paper is concerned with maximal subgroups of the ample (better known as topological full) groups of homeomorphisms of totally disconnected compact metrizable topological spaces. We describe all maximal subgroups that are stabilizers of finite sets. Under certain assumptions on the ample group (including minimality), we describe all maximal subgroups that are stabilizers of closed sets or stabilizers of partitions into clopen sets. In particular, our results apply to the ample groups associated with Cantor minimal systems. |
| title | On maximal subgroups of ample groups |
| topic | Group Theory Dynamical Systems 20E28, 20F38, 20F65, 37B02, 37B05 |
| url | https://arxiv.org/abs/2403.16364 |