{"id":"https://openalex.org/W2786172283","doi":"https://doi.org/10.1142/s0218196719500127","title":"Commutator subgroups of virtual and welded braid groups","display_name":"Commutator subgroups of virtual and welded braid groups","publication_year":2018,"publication_date":"2018-11-23","ids":{"openalex":"https://openalex.org/W2786172283","doi":"https://doi.org/10.1142/s0218196719500127","mag":"2786172283"},"language":"en","primary_location":{"id":"doi:10.1142/s0218196719500127","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196719500127","pdf_url":null,"source":{"id":"https://openalex.org/S23260266","display_name":"International Journal of Algebra and Computation","issn_l":"0218-1967","issn":["0218-1967","1793-6500"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Algebra and Computation","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1802.01383","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5110723055","display_name":"Valeriy G. Bardakov","orcid":null},"institutions":[{"id":"https://openalex.org/I188973947","display_name":"Novosibirsk State University","ror":"https://ror.org/04t2ss102","country_code":"RU","type":"education","lineage":["https://openalex.org/I188973947"]},{"id":"https://openalex.org/I4210096862","display_name":"Sobolev Institute of Mathematics","ror":"https://ror.org/00shc0s02","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I1313323035","https://openalex.org/I4210096862","https://openalex.org/I4210124601","https://openalex.org/I4210127387"]},{"id":"https://openalex.org/I3133424061","display_name":"Novosibirsk State Agricultural University","ror":"https://ror.org/01hgeey64","country_code":"RU","type":"education","lineage":["https://openalex.org/I3133424061"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"Valeriy G. Bardakov","raw_affiliation_strings":["Department of AOI, Novosibirsk State Agrarian University, Dobrolyubova Street, 160, Novosibirsk, 630039, Russia","Sobolev Institute of Mathematics and Novosibirsk State University, Novosibirsk 630090, Russia"],"affiliations":[{"raw_affiliation_string":"Department of AOI, Novosibirsk State Agrarian University, Dobrolyubova Street, 160, Novosibirsk, 630039, Russia","institution_ids":["https://openalex.org/I3133424061"]},{"raw_affiliation_string":"Sobolev Institute of Mathematics and Novosibirsk State University, Novosibirsk 630090, Russia","institution_ids":["https://openalex.org/I4210096862","https://openalex.org/I188973947"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5066085868","display_name":"Krishnendu Gongopadhyay","orcid":"https://orcid.org/0000-0003-4327-0660"},"institutions":[{"id":"https://openalex.org/I165916956","display_name":"Indian Institute of Science Education and Research Mohali","ror":"https://ror.org/01vztzd79","country_code":"IN","type":"education","lineage":["https://openalex.org/I165916956"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Krishnendu Gongopadhyay","raw_affiliation_strings":["Indian Institute of Science Education and Research (IISER) Mohali, Sector 81, S. A. S. Nagar, P. O. Manauli, Punjab 140306, India","Indian Institute of Science Education and Research (IISER) Mohali, Sector 81, S.A.S. Nagar, P.O. Manauli, Punjab 140306, India"],"affiliations":[{"raw_affiliation_string":"Indian Institute of Science Education and Research (IISER) Mohali, Sector 81, S. A. S. Nagar, P. O. Manauli, Punjab 140306, India","institution_ids":["https://openalex.org/I165916956"]},{"raw_affiliation_string":"Indian Institute of Science Education and Research (IISER) Mohali, Sector 81, S.A.S. Nagar, P.O. Manauli, Punjab 140306, India","institution_ids":["https://openalex.org/I165916956"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5067016070","display_name":"\u041c. \u0412. \u041d\u0435\u0449\u0430\u0434\u0438\u043c","orcid":"https://orcid.org/0000-0002-9463-7496"},"institutions":[{"id":"https://openalex.org/I4210096862","display_name":"Sobolev Institute of Mathematics","ror":"https://ror.org/00shc0s02","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I1313323035","https://openalex.org/I4210096862","https://openalex.org/I4210124601","https://openalex.org/I4210127387"]},{"id":"https://openalex.org/I188973947","display_name":"Novosibirsk State University","ror":"https://ror.org/04t2ss102","country_code":"RU","type":"education","lineage":["https://openalex.org/I188973947"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Mikhail V. Neshchadim","raw_affiliation_strings":["Sobolev Institute of Mathematics and Novosibirsk State University, Novosibirsk 630090, Russia","Sobolev Institute of Mathematics and Novosibirsk State University, Novosibirsk, 630090, Russia"],"affiliations":[{"raw_affiliation_string":"Sobolev Institute of Mathematics and Novosibirsk State University, Novosibirsk 630090, Russia","institution_ids":["https://openalex.org/I4210096862","https://openalex.org/I188973947"]},{"raw_affiliation_string":"Sobolev Institute of Mathematics and Novosibirsk State University, Novosibirsk, 630090, Russia","institution_ids":["https://openalex.org/I4210096862","https://openalex.org/I188973947"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5110723055"],"corresponding_institution_ids":["https://openalex.org/I188973947","https://openalex.org/I3133424061","https://openalex.org/I4210096862"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.08388122,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"29","issue":"03","first_page":"507","last_page":"533"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10304","display_name":"Geometric and Algebraic Topology","score":0.998199999332428,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10304","display_name":"Geometric and Algebraic Topology","score":0.998199999332428,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/commutator","display_name":"Commutator","score":0.830119788646698},{"id":"https://openalex.org/keywords/commutator-subgroup","display_name":"Commutator subgroup","score":0.6849594116210938},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6614179611206055},{"id":"https://openalex.org/keywords/braid-group","display_name":"Braid group","score":0.5636252164840698},{"id":"https://openalex.org/keywords/finitely-generated-abelian-group","display_name":"Finitely-generated abelian group","score":0.5389730334281921},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.4635635316371918},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.4305632710456848},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3341059386730194},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.2593100666999817},{"id":"https://openalex.org/keywords/normal-subgroup","display_name":"Normal subgroup","score":0.18443116545677185},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.13781675696372986},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.06049886345863342}],"concepts":[{"id":"https://openalex.org/C145620117","wikidata":"https://www.wikidata.org/wiki/Q2989763","display_name":"Commutator","level":4,"score":0.830119788646698},{"id":"https://openalex.org/C140865510","wikidata":"https://www.wikidata.org/wiki/Q522216","display_name":"Commutator subgroup","level":4,"score":0.6849594116210938},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6614179611206055},{"id":"https://openalex.org/C33840335","wikidata":"https://www.wikidata.org/wiki/Q220409","display_name":"Braid group","level":2,"score":0.5636252164840698},{"id":"https://openalex.org/C162860070","wikidata":"https://www.wikidata.org/wiki/Q142140","display_name":"Finitely-generated abelian group","level":2,"score":0.5389730334281921},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.4635635316371918},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.4305632710456848},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3341059386730194},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.2593100666999817},{"id":"https://openalex.org/C105515060","wikidata":"https://www.wikidata.org/wiki/Q743179","display_name":"Normal subgroup","level":3,"score":0.18443116545677185},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.13781675696372986},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.06049886345863342},{"id":"https://openalex.org/C73648015","wikidata":"https://www.wikidata.org/wiki/Q6543817","display_name":"Lie conformal algebra","level":3,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1142/s0218196719500127","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196719500127","pdf_url":null,"source":{"id":"https://openalex.org/S23260266","display_name":"International Journal of Algebra and Computation","issn_l":"0218-1967","issn":["0218-1967","1793-6500"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Algebra and Computation","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1802.01383","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1802.01383","pdf_url":"https://arxiv.org/pdf/1802.01383","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"mag:2786172283","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1802.01383.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1802.01383","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1802.01383","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1802.01383","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1802.01383","pdf_url":"https://arxiv.org/pdf/1802.01383","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2482387716","display_name":null,"funder_award_id":"INT/RUS/RSF/P-2","funder_id":"https://openalex.org/F4320320719","funder_display_name":"Department of Science and Technology, Ministry of Science and Technology, India"},{"id":"https://openalex.org/G4447180913","display_name":null,"funder_award_id":"16-41-02006","funder_id":"https://openalex.org/F4320324099","funder_display_name":"Russian Science Foundation"},{"id":"https://openalex.org/G8562469621","display_name":null,"funder_award_id":"N 16-41-02006","funder_id":"https://openalex.org/F4320324099","funder_display_name":"Russian Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320320719","display_name":"Department of Science and Technology, Ministry of Science and Technology, India","ror":"https://ror.org/0101xrq71"},{"id":"https://openalex.org/F4320324099","display_name":"Russian Science Foundation","ror":"https://ror.org/03y2gwe85"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2786172283.pdf","grobid_xml":"https://content.openalex.org/works/W2786172283.grobid-xml"},"referenced_works_count":9,"referenced_works":["https://openalex.org/W1968416168","https://openalex.org/W2024087012","https://openalex.org/W2091419649","https://openalex.org/W2094080661","https://openalex.org/W2156613167","https://openalex.org/W2766201438","https://openalex.org/W2962914109","https://openalex.org/W2963882728","https://openalex.org/W2964134343"],"related_works":["https://openalex.org/W2889177811","https://openalex.org/W2765212462","https://openalex.org/W2926036744","https://openalex.org/W3214197174","https://openalex.org/W1600717595","https://openalex.org/W2949258421","https://openalex.org/W2997059543","https://openalex.org/W2807162994","https://openalex.org/W2746867716","https://openalex.org/W3014637213","https://openalex.org/W2562981823","https://openalex.org/W2754998836","https://openalex.org/W2594609633","https://openalex.org/W2997712221","https://openalex.org/W2740423432","https://openalex.org/W1993965383","https://openalex.org/W2950714346","https://openalex.org/W2030730119","https://openalex.org/W2121668955","https://openalex.org/W2041269336"],"abstract_inverted_index":{"Let":[0],"[Formula:":[1,5,16,24,28,50,60,64,71,78,83,89,93],"see":[2,6,17,25,29,51,61,65,72,79,84,90,94],"text],":[3,30,62],"respectively":[4,11],"text]":[7,26,52,66,80,85,91,95],"denote":[8],"the":[9,86,99,105],"virtual,":[10],"welded,":[12],"braid":[13],"group":[14],"on":[15],"text]-strands.":[18],"We":[19,32],"study":[20],"their":[21],"commutator":[22,43,87,100,107],"subgroups":[23,88],"and,":[27],"respectively.":[31],"obtain":[33],"a":[34],"set":[35],"of":[36],"generators":[37],"and":[38,57,63,81,92],"defining":[39],"relations":[40],"for":[41,70,82],"these":[42],"subgroups.":[44],"In":[45],"particular,":[46],"we":[47,75],"prove":[48,76],"that":[49,77],"is":[53,67,102],"finitely":[54,68],"generated":[55,69],"if":[56,59],"only":[58],"text].":[73],"Also,":[74],"are":[96],"perfect,":[97],"i.e.":[98],"subgroup":[101],"equal":[103],"to":[104],"second":[106],"subgroup.":[108]},"counts_by_year":[{"year":2022,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}