{"id":"https://openalex.org/W2781742384","doi":"https://doi.org/10.1142/s0218196718400052","title":"Word maps on perfect algebraic groups","display_name":"Word maps on perfect algebraic groups","publication_year":2018,"publication_date":"2018-07-26","ids":{"openalex":"https://openalex.org/W2781742384","doi":"https://doi.org/10.1142/s0218196718400052","mag":"2781742384"},"language":"en","primary_location":{"id":"doi:10.1142/s0218196718400052","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196718400052","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/1801.00381","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5074001892","display_name":"Nikolai Gordeev","orcid":"https://orcid.org/0000-0002-5980-9344"},"institutions":[{"id":"https://openalex.org/I172901346","display_name":"St Petersburg University","ror":"https://ror.org/023znxa73","country_code":"RU","type":"education","lineage":["https://openalex.org/I172901346"]},{"id":"https://openalex.org/I4210101320","display_name":"Herzen University","ror":"https://ror.org/01e5ckr65","country_code":"RU","type":"education","lineage":["https://openalex.org/I4210101320"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"Nikolai Gordeev","raw_affiliation_strings":["Department of Mathematics of Sankt-Petersburg State University, 198504, Universitetsky Prospekt, 28, Peterhof, St. Petersburg, Russia","Department of Mathematics, Herzen State Pedagogical University, 48 Moika Embankment, 191186, St. Petersburg, Russia"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics of Sankt-Petersburg State University, 198504, Universitetsky Prospekt, 28, Peterhof, St. Petersburg, Russia","institution_ids":["https://openalex.org/I172901346"]},{"raw_affiliation_string":"Department of Mathematics, Herzen State Pedagogical University, 48 Moika Embankment, 191186, St. Petersburg, Russia","institution_ids":["https://openalex.org/I4210101320"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5039481706","display_name":"Boris Kunyavski\u0131\u0306","orcid":"https://orcid.org/0000-0002-9128-8729"},"institutions":[{"id":"https://openalex.org/I13955877","display_name":"Bar-Ilan University","ror":"https://ror.org/03kgsv495","country_code":"IL","type":"education","lineage":["https://openalex.org/I13955877"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Boris Kunyavski\u012d","raw_affiliation_strings":["Department of Mathematics, Bar-Ilan University, 5290002 Ramat Gan, Israel"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Bar-Ilan University, 5290002 Ramat Gan, Israel","institution_ids":["https://openalex.org/I13955877"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5108666320","display_name":"Eugene Plotkin","orcid":null},"institutions":[{"id":"https://openalex.org/I13955877","display_name":"Bar-Ilan University","ror":"https://ror.org/03kgsv495","country_code":"IL","type":"education","lineage":["https://openalex.org/I13955877"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Eugene Plotkin","raw_affiliation_strings":["Department of Mathematics, Bar-Ilan University, 5290002 Ramat Gan, Israel"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Bar-Ilan University, 5290002 Ramat Gan, Israel","institution_ids":["https://openalex.org/I13955877"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5074001892"],"corresponding_institution_ids":["https://openalex.org/I172901346","https://openalex.org/I4210101320"],"apc_list":null,"apc_paid":null,"fwci":2.8137,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.88909953,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"28","issue":"08","first_page":"1487","last_page":"1515"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10849","display_name":"Finite Group Theory Research","score":0.9993000030517578,"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"}},"topics":[{"id":"https://openalex.org/T10849","display_name":"Finite Group Theory Research","score":0.9993000030517578,"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/T11567","display_name":"semigroups and automata theory","score":0.9987999796867371,"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/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.9983999729156494,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/mathematics","display_name":"Mathematics","score":0.7121594548225403},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.6169450283050537},{"id":"https://openalex.org/keywords/word","display_name":"Word (group theory)","score":0.5153231024742126},{"id":"https://openalex.org/keywords/dominance","display_name":"Dominance (genetics)","score":0.4979431629180908},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.45621317625045776},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.437478244304657},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.049213558435440063},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.04016464948654175}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7121594548225403},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.6169450283050537},{"id":"https://openalex.org/C90805587","wikidata":"https://www.wikidata.org/wiki/Q10944557","display_name":"Word (group theory)","level":2,"score":0.5153231024742126},{"id":"https://openalex.org/C151913843","wikidata":"https://www.wikidata.org/wiki/Q3454555","display_name":"Dominance (genetics)","level":3,"score":0.4979431629180908},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.45621317625045776},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.437478244304657},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.049213558435440063},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.04016464948654175},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1142/s0218196718400052","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196718400052","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:1801.00381","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1801.00381","pdf_url":"https://arxiv.org/pdf/1801.00381","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":null,"raw_type":"text"},{"id":"pmh:oai:pure.mpg.de:item_3059934","is_oa":true,"landing_page_url":"http://hdl.handle.net/21.11116/0000-0003-AD0A-0","pdf_url":"https://pure.mpg.de/pubman/item/item_3059934_3/component/file_3059935/arXiv%3A1801.00381.pdf","source":{"id":"https://openalex.org/S4306400654","display_name":"MPG.PuRe (Max Planck Society)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I149899117","host_organization_name":"Max Planck Society","host_organization_lineage":["https://openalex.org/I149899117"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"International Journal of Algebra and Computation","raw_type":"info:eu-repo/semantics/article"},{"id":"mag:2781742384","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1801.00381.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.1801.00381","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1801.00381","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:1801.00381","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1801.00381","pdf_url":"https://arxiv.org/pdf/1801.00381","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":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":55,"referenced_works":["https://openalex.org/W46620492","https://openalex.org/W89883650","https://openalex.org/W1503569487","https://openalex.org/W1522780723","https://openalex.org/W1598525823","https://openalex.org/W1967998025","https://openalex.org/W1977278876","https://openalex.org/W1978656206","https://openalex.org/W1984208744","https://openalex.org/W1989356084","https://openalex.org/W1997326292","https://openalex.org/W2003522716","https://openalex.org/W2026304942","https://openalex.org/W2028774614","https://openalex.org/W2028983039","https://openalex.org/W2035235378","https://openalex.org/W2035483891","https://openalex.org/W2036451674","https://openalex.org/W2045568819","https://openalex.org/W2046262129","https://openalex.org/W2050625828","https://openalex.org/W2060489837","https://openalex.org/W2061175295","https://openalex.org/W2070198968","https://openalex.org/W2070225671","https://openalex.org/W2077199490","https://openalex.org/W2080440993","https://openalex.org/W2089316660","https://openalex.org/W2092735829","https://openalex.org/W2094162586","https://openalex.org/W2117985036","https://openalex.org/W2126521376","https://openalex.org/W2129651284","https://openalex.org/W2183410792","https://openalex.org/W2231660898","https://openalex.org/W2277578475","https://openalex.org/W2303904035","https://openalex.org/W2328147349","https://openalex.org/W2329713557","https://openalex.org/W2489093667","https://openalex.org/W2504646425","https://openalex.org/W2568909272","https://openalex.org/W2962740578","https://openalex.org/W2962951590","https://openalex.org/W2963086718","https://openalex.org/W2963106255","https://openalex.org/W2963261355","https://openalex.org/W2963927549","https://openalex.org/W2964007043","https://openalex.org/W3100577253","https://openalex.org/W3105673858","https://openalex.org/W3105871459","https://openalex.org/W4210405807","https://openalex.org/W4212890072","https://openalex.org/W4234165903"],"related_works":["https://openalex.org/W2135746628","https://openalex.org/W2787188914","https://openalex.org/W2980322410","https://openalex.org/W2163442287","https://openalex.org/W2500828598","https://openalex.org/W1674796559","https://openalex.org/W52712519","https://openalex.org/W128521600","https://openalex.org/W2152209113","https://openalex.org/W2071453418","https://openalex.org/W1578519308","https://openalex.org/W3755876","https://openalex.org/W2596692700","https://openalex.org/W2213930208","https://openalex.org/W31151545","https://openalex.org/W2114049252","https://openalex.org/W1636987159","https://openalex.org/W2982105761","https://openalex.org/W3112933313","https://openalex.org/W3000070000"],"abstract_inverted_index":{"We":[0,30],"extend":[1],"Borel\u2019s":[2,23],"theorem":[3,24],"on":[4,59],"the":[5,33],"dominance":[6],"of":[7,45],"word":[8],"maps":[9],"from":[10],"semisimple":[11],"algebraic":[12],"groups":[13],"to":[14,25],"some":[15,26,49],"perfect":[16],"groups.":[17],"In":[18],"another":[19],"direction,":[20],"we":[21],"generalize":[22],"words":[27,38],"with":[28,57],"constants.":[29],"also":[31],"consider":[32],"surjectivity":[34],"problem":[35],"for":[36],"particular":[37],"and":[39,51,53,63],"groups,":[40],"give":[41],"a":[42],"brief":[43],"survey":[44],"recent":[46],"results,":[47],"present":[48],"generalizations":[50],"variations":[52],"discuss":[54],"various":[55],"approaches,":[56],"emphasis":[58],"new":[60],"ideas,":[61],"constructions":[62],"connections.":[64]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":1}],"updated_date":"2026-03-10T16:38:18.471706","created_date":"2025-10-10T00:00:00"}
