Multi-virtual braid groups
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866910051092922368 |
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| author | Bardakov, Valeriy G. Kozlovskaya, Tatyana A. Negi, Komal Prabhakar, Madeti |
| author_facet | Bardakov, Valeriy G. Kozlovskaya, Tatyana A. Negi, Komal Prabhakar, Madeti |
| contents | L. Kauffman (2024) introduced multi-virtual and symmetric multi-virtual braid groups, which are generalizations of the virtual braid group. We introduce multi-virtual pure and multi-virtual semi-pure braid groups, which are normal subgroups of index $n!$. We give a set of generators and defining relations for these groups, show that multi-virtual (symmetric multi-virtual) braid group is a semi-direct products of multi-virtual pure (symmetric multi-virtual pure) braid group and symmetric group. Also, we introduce multi-welded and multi-unrestricted braid groups and examines structure of three-strand 2-virtual braid group and some its subgroups and quotients. The paper concludes by outlining open problems and suggesting avenues for future research in this area. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_14551 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Multi-virtual braid groups Bardakov, Valeriy G. Kozlovskaya, Tatyana A. Negi, Komal Prabhakar, Madeti Group Theory General Topology 20E07, 20F36, 57K12 L. Kauffman (2024) introduced multi-virtual and symmetric multi-virtual braid groups, which are generalizations of the virtual braid group. We introduce multi-virtual pure and multi-virtual semi-pure braid groups, which are normal subgroups of index $n!$. We give a set of generators and defining relations for these groups, show that multi-virtual (symmetric multi-virtual) braid group is a semi-direct products of multi-virtual pure (symmetric multi-virtual pure) braid group and symmetric group. Also, we introduce multi-welded and multi-unrestricted braid groups and examines structure of three-strand 2-virtual braid group and some its subgroups and quotients. The paper concludes by outlining open problems and suggesting avenues for future research in this area. |
| title | Multi-virtual braid groups |
| topic | Group Theory General Topology 20E07, 20F36, 57K12 |
| url | https://arxiv.org/abs/2507.14551 |