<abstract xmlns="http://www.w3.org/1999/xhtml">

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.
</abstract>

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

Published Online: May 27, 2024

Page range: 183 - 200

Received: Jan 21, 2023

Accepted: May 15, 2023

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

Keywords
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

Published Online: May 27, 2024

Page range: 183 - 200

Received: Jan 21, 2023

Accepted: May 15, 2023

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

KeywordsBraid, 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.

Keywords
Braid, braid of braids, unrestricted virtual singular braid, representations of braid structures