Metric ultraproducts of groups -- simplicity, perfectness and torsion
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arXiv
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| Format: | Preprint |
| Published: |
2020
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| _version_ | 1866914958105640960 |
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| author | Gismatullin, Jakub Majcher, Krzysztof Ziegler, Martin |
| author_facet | Gismatullin, Jakub Majcher, Krzysztof Ziegler, Martin |
| contents | We characterise the simplicity of metric ultraproducts of a family of metric groups. We also present several new examples of simple groups, such as metric ultraproducts of finite and infinite symmetric groups, linear groups, and interval exchange transformation groups. Using similar methods, we also examine concepts such as genericity, perfectness, and torsion. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2010_03394 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Metric ultraproducts of groups -- simplicity, perfectness and torsion Gismatullin, Jakub Majcher, Krzysztof Ziegler, Martin Group Theory Logic Metric Geometry 20E32, 20E45, 03C20, 12L10 We characterise the simplicity of metric ultraproducts of a family of metric groups. We also present several new examples of simple groups, such as metric ultraproducts of finite and infinite symmetric groups, linear groups, and interval exchange transformation groups. Using similar methods, we also examine concepts such as genericity, perfectness, and torsion. |
| title | Metric ultraproducts of groups -- simplicity, perfectness and torsion |
| topic | Group Theory Logic Metric Geometry 20E32, 20E45, 03C20, 12L10 |
| url | https://arxiv.org/abs/2010.03394 |