Twisted Virtual Braid Group Full article
| Journal |
Journal of Knot Theory and its Ramifications
ISSN: 0218-2165 |
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| Output data | Year: 2025, Article number : 2550028, Pages count : 21 DOI: 10.1142/s0218216525500282 | ||||||
| Tags | Twisted virtual braid group; twisted virtual pure braid group; Reidemeister-Schreier method | ||||||
| Authors |
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| Affiliations |
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Funding (2)
| 1 | Sobolev Institute of Mathematics | FWNF-2022-0009 |
| 2 | Фонд развития теоретической физики и математики «БАЗИС» | 23-7-2-14-1 |
Abstract:
In this paper, we study some subgroups and their decompositions in semi-direct product of the twisted virtual braid group TVBn. In particular, the twisted virtual pure braid group TVPn is the kernel of an epimorphism of TVBn onto the symmetric group Sn. We find the set of generators and defining relations for TVPn and show that TVBn =TVPn Sn. Further, we prove that TVPn is a semi-direct product of some subgroup and abelian group Zn 2. As a corollary, we get that the virtual pure braid group VPn is a subgroup of TVPn. Also, we construct some other epimorphism of TVBn onto Sn. Its kernel TVHn is an analogous of TVPn. We find its set of generators and define relations and construct their decomposition in a semi-direct product.
Cite:
Bardakov V.G.
, Kozlovskaya T.A.
, Negi K.
, Prabhakar M.
Twisted Virtual Braid Group
Journal of Knot Theory and its Ramifications. 2025. 2550028 :1-21. DOI: 10.1142/s0218216525500282 WOS Scopus OpenAlex
Twisted Virtual Braid Group
Journal of Knot Theory and its Ramifications. 2025. 2550028 :1-21. DOI: 10.1142/s0218216525500282 WOS Scopus OpenAlex
Dates:
| Submitted: | Oct 10, 2023 |
| Accepted: | Mar 26, 2025 |
| Published online: | May 21, 2025 |
Identifiers:
| Web of science: | WOS:001494040100001 |
| Scopus: | 2-s2.0-105006532583 |
| OpenAlex: | W4409170582 |
Citing:
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