Subgroup Separability of Artin Groups II
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909132669321216 |
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| author | Almeida, Kisnney Lima, Igor |
| author_facet | Almeida, Kisnney Lima, Igor |
| contents | In this paper, we establish a new criterion for determining whether an Artin group is subgroup separable (LERF), building upon a criterion introduced in a previous work. Specifically, we prove an Artin group is LERF if and only if it does not contain certain induced subgraphs, thus providing a more direct generalization of the Metaftsis-Raptis criterion for RAAGs. As consequences, we prove an Artin group is ERF if and only if it is a free abelian group and we establish a link between subgroup separability and coherence for Artin groups. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2403_05483 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Subgroup Separability of Artin Groups II Almeida, Kisnney Lima, Igor Group Theory 20F36, 20E26 In this paper, we establish a new criterion for determining whether an Artin group is subgroup separable (LERF), building upon a criterion introduced in a previous work. Specifically, we prove an Artin group is LERF if and only if it does not contain certain induced subgraphs, thus providing a more direct generalization of the Metaftsis-Raptis criterion for RAAGs. As consequences, we prove an Artin group is ERF if and only if it is a free abelian group and we establish a link between subgroup separability and coherence for Artin groups. |
| title | Subgroup Separability of Artin Groups II |
| topic | Group Theory 20F36, 20E26 |
| url | https://arxiv.org/abs/2403.05483 |