{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,5,29]],"date-time":"2024-05-29T22:31:31Z","timestamp":1717021891732},"reference-count":13,"publisher":"World Scientific Pub Co Pte Lt","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2019,5]]},"abstract":"<jats:p> Let [Formula: see text], respectively [Formula: see text] denote the virtual, respectively welded, braid group on [Formula: see text]-strands. We study their commutator subgroups [Formula: see text] and, [Formula: see text], respectively. We obtain a set of generators and defining relations for these commutator subgroups. In particular, we prove that [Formula: see text] is finitely generated if and only if [Formula: see text], and [Formula: see text] is finitely generated for [Formula: see text]. Also, we prove that [Formula: see text] and for [Formula: see text] the commutator subgroups [Formula: see text] and [Formula: see text] are perfect, i.e. the commutator subgroup is equal to the second commutator subgroup. <\/jats:p>","DOI":"10.1142\/s0218196719500127","type":"journal-article","created":{"date-parts":[[2018,11,23]],"date-time":"2018-11-23T06:59:10Z","timestamp":1542956350000},"page":"507-533","source":"Crossref","is-referenced-by-count":2,"title":["Commutator subgroups of virtual and welded braid groups"],"prefix":"10.1142","volume":"29","author":[{"given":"Valeriy G.","family":"Bardakov","sequence":"first","affiliation":[{"name":"Sobolev Institute of Mathematics and Novosibirsk State University, Novosibirsk 630090, Russia"},{"name":"Department of AOI, Novosibirsk State Agrarian University, Dobrolyubova Street, 160, Novosibirsk, 630039, Russia"}]},{"given":"Krishnendu","family":"Gongopadhyay","sequence":"additional","affiliation":[{"name":"Indian Institute of Science Education and Research (IISER) Mohali, Sector 81, S. A. S. Nagar, P. O. Manauli, Punjab 140306, India"}]},{"given":"Mikhail V.","family":"Neshchadim","sequence":"additional","affiliation":[{"name":"Sobolev Institute of Mathematics and Novosibirsk State University, Novosibirsk 630090, Russia"}]}],"member":"219","published-online":{"date-parts":[[2019,5,29]]},"reference":[{"key":"S0218196719500127BIB002","doi-asserted-by":"publisher","DOI":"10.4064\/fm184-0-1"},{"key":"S0218196719500127BIB003","doi-asserted-by":"publisher","DOI":"10.1134\/S0037446617050032"},{"key":"S0218196719500127BIB004","doi-asserted-by":"publisher","DOI":"10.1142\/S0218216517500031"},{"key":"S0218196719500127BIB005","doi-asserted-by":"publisher","DOI":"10.1016\/j.topol.2008.10.002"},{"key":"S0218196719500127BIB006","doi-asserted-by":"publisher","DOI":"10.1016\/j.exmath.2016.12.003"},{"key":"S0218196719500127BIB007","doi-asserted-by":"publisher","DOI":"10.1016\/j.topol.2018.01.003"},{"key":"S0218196719500127BIB008","doi-asserted-by":"publisher","DOI":"10.1016\/0040-9383(95)00072-0"},{"issue":"120","key":"S0218196719500127BIB009","first-page":"579","volume":"78","author":"Gorin E. A.","year":"1969","journal-title":"Mat. Sb. (N.S.)"},{"issue":"2","key":"S0218196719500127BIB010","first-page":"441","volume":"44","author":"Kamada S.","year":"2007","journal-title":"Osaka J. Math."},{"key":"S0218196719500127BIB011","doi-asserted-by":"publisher","DOI":"10.1006\/eujc.1999.0314"},{"key":"S0218196719500127BIB012","volume-title":"Combinatorial Group Theory","author":"Magnus W.","year":"2004","edition":"2"},{"key":"S0218196719500127BIB013","first-page":"11","volume":"118","author":"Savushkina A. G.","year":"1994","journal-title":"Vestnik Moskov. Univ. Ser. I Mat. Mekh."},{"key":"S0218196719500127BIB015","doi-asserted-by":"publisher","DOI":"10.1142\/S0218216501001165"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196719500127","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T17:24:43Z","timestamp":1565198683000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196719500127"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,5]]},"references-count":13,"journal-issue":{"issue":"03","published-online":{"date-parts":[[2019,5,29]]},"published-print":{"date-parts":[[2019,5]]}},"alternative-id":["10.1142\/S0218196719500127"],"URL":"https:\/\/doi.org\/10.1142\/s0218196719500127","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,5]]}}}