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- Title
Commutator subgroups of singular braid groups.
- Authors
Dey, Soumya; Gongopadhyay, Krishnendu
- Abstract
The singular braids with n strands, n ≥ 3 , were introduced independently by Baez and Birman. It is known that the monoid formed by the singular braids is embedded in a group that is known as singular braid group, denoted by S G n . There has been another generalization of braid groups, denoted by G V B n , n ≥ 3 , which was introduced by Fang as a group of symmetries behind quantum quasi-shuffle structures. The group G V B n simultaneously generalizes the classical braid group, as well as the virtual braid group on n strands. We investigate the commutator subgroups S G n ′ and G V B n ′ of these generalized braid groups. We prove that S G n ′ is finitely generated if and only if n ≥ 5 , and G V B n ′ is finitely generated if and only if n ≥ 4. Further, we show that both S G n ′ and G V B n ′ are perfect if and only if n ≥ 5.
- Subjects
COMMUTATION (Electricity); GROUPOIDS; SYMMETRY groups
- Publication
Journal of Knot Theory & Its Ramifications, 2022, Vol 31, Issue 5, p1
- ISSN
0218-2165
- Publication type
Article
- DOI
10.1142/S021821652250033X