{"id":"https://openalex.org/W2023468821","doi":"https://doi.org/10.1142/s0218196709005329","title":"ONE-SIDE NIELSEN TRANSFORMATIONS IN FREE GROUPS","display_name":"ONE-SIDE NIELSEN TRANSFORMATIONS IN FREE GROUPS","publication_year":2009,"publication_date":"2009-11-01","ids":{"openalex":"https://openalex.org/W2023468821","doi":"https://doi.org/10.1142/s0218196709005329","mag":"2023468821"},"language":"en","primary_location":{"id":"doi:10.1142/s0218196709005329","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196709005329","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":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5039946470","display_name":"Alexei Vernitski","orcid":"https://orcid.org/0000-0003-0179-9099"},"institutions":[{"id":"https://openalex.org/I110002522","display_name":"University of Essex","ror":"https://ror.org/02nkf1q06","country_code":"GB","type":"education","lineage":["https://openalex.org/I110002522"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"ALEXEI VERNITSKI","raw_affiliation_strings":["Department of Mathematical Sciences, University of Essex, Colchester, United Kingdom, CO4 3SQ, UK"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, University of Essex, Colchester, United Kingdom, CO4 3SQ, UK","institution_ids":["https://openalex.org/I110002522"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5039946470"],"corresponding_institution_ids":["https://openalex.org/I110002522"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.10314319,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"19","issue":"07","first_page":"855","last_page":"871"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9786999821662903,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9786999821662903,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10849","display_name":"Finite Group Theory Research","score":0.9739000201225281,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11611","display_name":"Cyclopropane Reaction Mechanisms","score":0.9596999883651733,"subfield":{"id":"https://openalex.org/subfields/1605","display_name":"Organic Chemistry"},"field":{"id":"https://openalex.org/fields/16","display_name":"Chemistry"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8900750875473022},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7750120162963867},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.6045886278152466},{"id":"https://openalex.org/keywords/connected-component","display_name":"Connected component","score":0.5432021617889404},{"id":"https://openalex.org/keywords/distance-regular-graph","display_name":"Distance-regular graph","score":0.46030759811401367},{"id":"https://openalex.org/keywords/connectivity","display_name":"Connectivity","score":0.4485185146331787},{"id":"https://openalex.org/keywords/graph-power","display_name":"Graph power","score":0.4216771721839905},{"id":"https://openalex.org/keywords/complement-graph","display_name":"Complement graph","score":0.4107140302658081},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3697648048400879},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.2582470774650574}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8900750875473022},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7750120162963867},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.6045886278152466},{"id":"https://openalex.org/C193435613","wikidata":"https://www.wikidata.org/wiki/Q2997928","display_name":"Connected component","level":2,"score":0.5432021617889404},{"id":"https://openalex.org/C56783289","wikidata":"https://www.wikidata.org/wiki/Q3115556","display_name":"Distance-regular graph","level":5,"score":0.46030759811401367},{"id":"https://openalex.org/C76444178","wikidata":"https://www.wikidata.org/wiki/Q72897900","display_name":"Connectivity","level":3,"score":0.4485185146331787},{"id":"https://openalex.org/C149530733","wikidata":"https://www.wikidata.org/wiki/Q5597091","display_name":"Graph power","level":4,"score":0.4216771721839905},{"id":"https://openalex.org/C168291704","wikidata":"https://www.wikidata.org/wiki/Q902252","display_name":"Complement graph","level":5,"score":0.4107140302658081},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3697648048400879},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.2582470774650574}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s0218196709005329","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196709005329","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:repository.essex.ac.uk:1804","is_oa":false,"landing_page_url":"http://repository.essex.ac.uk/1804/","pdf_url":null,"source":{"id":"https://openalex.org/S4306401236","display_name":"Open Access at Essex (University of Essex)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I110002522","host_organization_name":"University of Essex","host_organization_lineage":["https://openalex.org/I110002522"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":4,"referenced_works":["https://openalex.org/W1234885875","https://openalex.org/W2026468639","https://openalex.org/W2042262709","https://openalex.org/W2053384159"],"related_works":["https://openalex.org/W2804933047","https://openalex.org/W4298388358","https://openalex.org/W2806499800","https://openalex.org/W2004791814","https://openalex.org/W4287724105","https://openalex.org/W3040845265","https://openalex.org/W2278094798","https://openalex.org/W2070569225","https://openalex.org/W2359658485","https://openalex.org/W3157164550"],"abstract_inverted_index":{"We":[0,65],"study":[1,66],"a":[2,16,33,83],"graph":[3,71],"related":[4],"to":[5,51,92],"the":[6,45,70,74,93,98],"Andrews\u2014Curtis":[7],"graph.":[8,99],"The":[9],"vertices":[10,21],"are":[11,22],"pairs":[12,76,90],"of":[13,15,69,97],"elements":[14],"free":[17],"group,":[18],"and":[19,60,72],"two":[20,41,89],"adjacent":[23,50],"if":[24],"they":[25],"can":[26],"be":[27],"obtained":[28],"from":[29],"one":[30],"another":[31],"by":[32],"left":[34],"Nielsen":[35],"transformation,":[36],"that":[37],"is,":[38],"for":[39,86],"each":[40],"words":[42],"u,":[43,56],"v":[44],"pair":[46],"(u,":[47,58,61],"v)":[48],"is":[49],"(vu,":[52],"v),":[53,57],"(v":[54],"\u20111":[55,63],"uv),":[59],"u":[62],"v).":[64],"connected":[67,95],"components":[68],"describe":[73],"shortest":[75],"in":[77],"all":[78],"components.":[79],"Hence,":[80],"we":[81],"find":[82],"linear-time":[84],"algorithm":[85],"checking":[87],"whether":[88],"belong":[91],"same":[94],"component":[96]},"counts_by_year":[],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}
