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Let <italic>n, m</italic> ∈ ℕ, <italic>n</italic> ≥ 3 and <italic>n</italic> ≥ <italic>m</italic> ≥ 2. In this paper, we study some properties of the unrestricted virtual singular braid of braid monoid <italic><bold>UVSB</bold>mn</italic> and group <bold><italic>UVSG</italic></bold><italic>mn</italic>. These properties emerged by studying the analogous properties of the unrestricted virtual singular pseudosymmetric braid of braid monoid and group. These mathematical objects are submonoids and subgroups of the virtual singular braid group <italic>VSGn</italic>. For many of these quotients, we have obtained reduced presentations.
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Let n, m ∈ ℕ, n ≥ 3 and n ≥ m ≥ 2. In this paper, we study some properties of the unrestricted virtual singular braid of braid monoid UVSBmn and group UVSGmn. These properties emerged by studying the analogous properties of the unrestricted virtual singular pseudosymmetric braid of braid monoid and group. These mathematical objects are submonoids and subgroups of the virtual singular braid group VSGn. For many of these quotients, we have obtained reduced presentations.

On the unrestricted virtual singular braid

Departamento lgebra, Geometra y Topologa, Facultad de Ciencias

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

{"article-title":"On the unrestricted virtual singular braid"}

Let n, m ∈ ℕ, n ≥ 3 and n ≥ m ≥ 2. In this paper, we study some properties of the unrestricted virtual singular braid of braid monoid UVSBmn and group UVSGmn....

On the unrestricted virtual singular braid

Publié en ligne: 27 mai 2024

Pages: 183 - 200

Reçu: 21 janv. 2023

Accepté: 15 mai 2023

DOI: https://doi.org/10.2478/auom-2024-0010

Mots clés
Braid, braid of braids, unrestricted virtual singular braid, representations of braid structures

© 2024 Panagiote Ligouras, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

On the unrestricted virtual singular braid

Publié en ligne: 27 mai 2024

Pages: 183 - 200

Reçu: 21 janv. 2023

Accepté: 15 mai 2023

DOI: https://doi.org/10.2478/auom-2024-0010

Mots clésBraid, braid of braids, unrestricted virtual singular braid, representations of braid structures

© 2024 Panagiote Ligouras, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Mots clés
Braid, braid of braids, unrestricted virtual singular braid, representations of braid structures