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Commutator subgroups of virtual and welded braid groups. / Bardakov, Valeriy G.; Gongopadhyay, Krishnendu; Neshchadim, Mikhail V.

In: International Journal of Algebra and Computation, Vol. 29, No. 3, 01.05.2019, p. 507-533.

Research output: Contribution to journalArticlepeer-review

Harvard

Bardakov, VG, Gongopadhyay, K & Neshchadim, MV 2019, 'Commutator subgroups of virtual and welded braid groups', International Journal of Algebra and Computation, vol. 29, no. 3, pp. 507-533. https://doi.org/10.1142/S0218196719500127

APA

Bardakov, V. G., Gongopadhyay, K., & Neshchadim, M. V. (2019). Commutator subgroups of virtual and welded braid groups. International Journal of Algebra and Computation, 29(3), 507-533. https://doi.org/10.1142/S0218196719500127

Vancouver

Bardakov VG, Gongopadhyay K, Neshchadim MV. Commutator subgroups of virtual and welded braid groups. International Journal of Algebra and Computation. 2019 May 1;29(3):507-533. doi: 10.1142/S0218196719500127

Author

Bardakov, Valeriy G. ; Gongopadhyay, Krishnendu ; Neshchadim, Mikhail V. / Commutator subgroups of virtual and welded braid groups. In: International Journal of Algebra and Computation. 2019 ; Vol. 29, No. 3. pp. 507-533.

BibTeX

@article{dd96e72f401f4e779c0e0a5a208eb46c,
title = "Commutator subgroups of virtual and welded braid groups",
abstract = "Let VBn, respectively WBn denote the virtual, respectively welded, braid group on n-strands. We study their commutator subgroups VB n = [VBn,VBn] and, WB n = [WBn,WBn], respectively. We obtain a set of generators and defining relations for these commutator subgroups. In particular, we prove that VB n is finitely generated if and only if n = 4, and WB n is finitely generated for n = 3. Also, we prove that VB 3/VB 3 = Z3 Z3Z3Z 8,VB 4/VB 4 = Z3Z3Z3,WB 3/WB 3 = Z3Z3Z3Z,WB 4/WB 4 = Z3, and for n = 5 the commutator subgroups VB n andWB n are perfect, i.e. the commutator subgroup is equal to the second commutator subgroup.",
keywords = "commutator subgroup, perfect group, Virtual braid, welded braid",
author = "Bardakov, {Valeriy G.} and Krishnendu Gongopadhyay and Neshchadim, {Mikhail V.}",
year = "2019",
month = may,
day = "1",
doi = "10.1142/S0218196719500127",
language = "English",
volume = "29",
pages = "507--533",
journal = "International Journal of Algebra and Computation",
issn = "0218-1967",
publisher = "World Scientific Publishing Co. Pte Ltd",
number = "3",

}

RIS

TY - JOUR

T1 - Commutator subgroups of virtual and welded braid groups

AU - Bardakov, Valeriy G.

AU - Gongopadhyay, Krishnendu

AU - Neshchadim, Mikhail V.

PY - 2019/5/1

Y1 - 2019/5/1

N2 - Let VBn, respectively WBn denote the virtual, respectively welded, braid group on n-strands. We study their commutator subgroups VB n = [VBn,VBn] and, WB n = [WBn,WBn], respectively. We obtain a set of generators and defining relations for these commutator subgroups. In particular, we prove that VB n is finitely generated if and only if n = 4, and WB n is finitely generated for n = 3. Also, we prove that VB 3/VB 3 = Z3 Z3Z3Z 8,VB 4/VB 4 = Z3Z3Z3,WB 3/WB 3 = Z3Z3Z3Z,WB 4/WB 4 = Z3, and for n = 5 the commutator subgroups VB n andWB n are perfect, i.e. the commutator subgroup is equal to the second commutator subgroup.

AB - Let VBn, respectively WBn denote the virtual, respectively welded, braid group on n-strands. We study their commutator subgroups VB n = [VBn,VBn] and, WB n = [WBn,WBn], respectively. We obtain a set of generators and defining relations for these commutator subgroups. In particular, we prove that VB n is finitely generated if and only if n = 4, and WB n is finitely generated for n = 3. Also, we prove that VB 3/VB 3 = Z3 Z3Z3Z 8,VB 4/VB 4 = Z3Z3Z3,WB 3/WB 3 = Z3Z3Z3Z,WB 4/WB 4 = Z3, and for n = 5 the commutator subgroups VB n andWB n are perfect, i.e. the commutator subgroup is equal to the second commutator subgroup.

KW - commutator subgroup

KW - perfect group

KW - Virtual braid

KW - welded braid

UR - http://www.scopus.com/inward/record.url?scp=85058222429&partnerID=8YFLogxK

U2 - 10.1142/S0218196719500127

DO - 10.1142/S0218196719500127

M3 - Article

AN - SCOPUS:85058222429

VL - 29

SP - 507

EP - 533

JO - International Journal of Algebra and Computation

JF - International Journal of Algebra and Computation

SN - 0218-1967

IS - 3

ER -

ID: 20346410