TY - JOUR

T1 - On 3-strand singular pure braid group

AU - Bardakov, Valeriy G.

AU - Kozlovskaya, Tatyana A.

N1 - Publisher Copyright: © 2020 World Scientific Publishing Company. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2020/9

Y1 - 2020/9

N2 - In this paper, we study the singular pure braid group SPn for n = 2, 3. We find generators, defining relations and the algebraical structure of these groups. In particular, we prove that SP3 is a semi-direct product SP3 = V3, where V3 is an HNN-extension with base group;2-Z&2 and cyclic associated subgroups. We prove that the center Z(SP3) of SP3 is a direct factor in SP3.

AB - In this paper, we study the singular pure braid group SPn for n = 2, 3. We find generators, defining relations and the algebraical structure of these groups. In particular, we prove that SP3 is a semi-direct product SP3 = V3, where V3 is an HNN-extension with base group;2-Z&2 and cyclic associated subgroups. We prove that the center Z(SP3) of SP3 is a direct factor in SP3.

KW - Braid group

KW - monoid of singular braids

KW - singular pure braid group

KW - MONOIDS

UR - http://www.scopus.com/inward/record.url?scp=85092071457&partnerID=8YFLogxK

U2 - 10.1142/S0218216520420018

DO - 10.1142/S0218216520420018

M3 - Article

AN - SCOPUS:85092071457

VL - 29

JO - Journal of Knot Theory and its Ramifications

JF - Journal of Knot Theory and its Ramifications

SN - 0218-2165

IS - 10

M1 - 2042001

ER -