Generalized Residual Finiteness of Groups
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866916086567403520 |
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| author | Brody, Nic Jankiewicz, Kasia |
| author_facet | Brody, Nic Jankiewicz, Kasia |
| contents | A countable group is residually finite if every nontrivial element can act nontrivially on a finite set. When a group fails to be residually finite, we might want to measure how drastically it fails - it could be that only finitely many conjugacy classes of elements fail to act nontrivially on a finite set, or it could be that the group has no nontrivial actions on finite sets whatsoever. We define a hierarchy of properties, and construct groups which become arbitrarily complicated in this sense. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_15120 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Generalized Residual Finiteness of Groups Brody, Nic Jankiewicz, Kasia Group Theory 20E26, 20F65 A countable group is residually finite if every nontrivial element can act nontrivially on a finite set. When a group fails to be residually finite, we might want to measure how drastically it fails - it could be that only finitely many conjugacy classes of elements fail to act nontrivially on a finite set, or it could be that the group has no nontrivial actions on finite sets whatsoever. We define a hierarchy of properties, and construct groups which become arbitrarily complicated in this sense. |
| title | Generalized Residual Finiteness of Groups |
| topic | Group Theory 20E26, 20F65 |
| url | https://arxiv.org/abs/2312.15120 |