{"id":"https://openalex.org/W1991702245","doi":"https://doi.org/10.1016/s0304-3975(03)00093-8","title":"Image reducing words and subgroups of free groups","display_name":"Image reducing words and subgroups of free groups","publication_year":2003,"publication_date":"2003-04-07","ids":{"openalex":"https://openalex.org/W1991702245","doi":"https://doi.org/10.1016/s0304-3975(03)00093-8","mag":"1991702245"},"language":"en","primary_location":{"id":"doi:10.1016/s0304-3975(03)00093-8","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0304-3975(03)00093-8","pdf_url":null,"source":{"id":"https://openalex.org/S90727058","display_name":"Theoretical Computer Science","issn_l":"0304-3975","issn":["0304-3975","1879-2294"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theoretical Computer Science","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/A5113930511","display_name":"D. S. Ananichev","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"D.S. Ananichev","raw_affiliation_strings":["Department of Mathematics and Mechanics, Ural State University, 620083 Ekaterinburg, Russia"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Mechanics, Ural State University, 620083 Ekaterinburg, Russia","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5111008563","display_name":"A. Cherubini","orcid":null},"institutions":[{"id":"https://openalex.org/I93860229","display_name":"Politecnico di Milano","ror":"https://ror.org/01nffqt88","country_code":"IT","type":"education","lineage":["https://openalex.org/I93860229"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"A. Cherubini","raw_affiliation_strings":["Dipartimento di Matematica \u201cFrancesco Brioschi\u201d, Politecnico di Milano, 20133 Milano, Italy"],"affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica \u201cFrancesco Brioschi\u201d, Politecnico di Milano, 20133 Milano, Italy","institution_ids":["https://openalex.org/I93860229"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5079604981","display_name":"Mikhail V. Volkov","orcid":"https://orcid.org/0000-0002-9327-243X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"M.V. Volkov","raw_affiliation_strings":["Department of Mathematics and Mechanics, Ural State University, 620083 Ekaterinburg, Russia"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Mechanics, Ural State University, 620083 Ekaterinburg, Russia","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5111008563"],"corresponding_institution_ids":["https://openalex.org/I93860229"],"apc_list":{"value":2690,"currency":"USD","value_usd":2690},"apc_paid":null,"fwci":3.6344,"has_fulltext":false,"cited_by_count":17,"citation_normalized_percentile":{"value":0.9290591,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"307","issue":"1","first_page":"77","last_page":"92"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9998999834060669,"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":0.9998999834060669,"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/T10304","display_name":"Geometric and Algebraic Topology","score":0.9991000294685364,"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"}},{"id":"https://openalex.org/T12029","display_name":"DNA and Biological Computing","score":0.9807000160217285,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/word","display_name":"Word (group theory)","score":0.7959567308425903},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6913884878158569},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.6379843950271606},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6033048033714294},{"id":"https://openalex.org/keywords/free-group","display_name":"Free group","score":0.5821356773376465},{"id":"https://openalex.org/keywords/alphabet","display_name":"Alphabet","score":0.5786274671554565},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5165368914604187},{"id":"https://openalex.org/keywords/free-product","display_name":"Free product","score":0.5064994096755981},{"id":"https://openalex.org/keywords/characterization","display_name":"Characterization (materials science)","score":0.5043700933456421},{"id":"https://openalex.org/keywords/finitely-generated-abelian-group","display_name":"Finitely-generated abelian group","score":0.49054068326950073},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4710685610771179},{"id":"https://openalex.org/keywords/word-problem","display_name":"Word problem (mathematics education)","score":0.46108290553092957},{"id":"https://openalex.org/keywords/finitely-generated-group","display_name":"Finitely generated group","score":0.448606014251709},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.42169252038002014},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.29050400853157043},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.17265325784683228},{"id":"https://openalex.org/keywords/linguistics","display_name":"Linguistics","score":0.1176542341709137},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.07553470134735107}],"concepts":[{"id":"https://openalex.org/C90805587","wikidata":"https://www.wikidata.org/wiki/Q10944557","display_name":"Word (group theory)","level":2,"score":0.7959567308425903},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6913884878158569},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.6379843950271606},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6033048033714294},{"id":"https://openalex.org/C77021192","wikidata":"https://www.wikidata.org/wiki/Q431078","display_name":"Free group","level":3,"score":0.5821356773376465},{"id":"https://openalex.org/C112876837","wikidata":"https://www.wikidata.org/wiki/Q837518","display_name":"Alphabet","level":2,"score":0.5786274671554565},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5165368914604187},{"id":"https://openalex.org/C47527751","wikidata":"https://www.wikidata.org/wiki/Q1454165","display_name":"Free product","level":3,"score":0.5064994096755981},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.5043700933456421},{"id":"https://openalex.org/C162860070","wikidata":"https://www.wikidata.org/wiki/Q142140","display_name":"Finitely-generated abelian group","level":2,"score":0.49054068326950073},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4710685610771179},{"id":"https://openalex.org/C90988201","wikidata":"https://www.wikidata.org/wiki/Q255912","display_name":"Word problem (mathematics education)","level":2,"score":0.46108290553092957},{"id":"https://openalex.org/C2780811992","wikidata":"https://www.wikidata.org/wiki/Q21083858","display_name":"Finitely generated group","level":3,"score":0.448606014251709},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.42169252038002014},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.29050400853157043},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.17265325784683228},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.1176542341709137},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.07553470134735107},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C171250308","wikidata":"https://www.wikidata.org/wiki/Q11468","display_name":"Nanotechnology","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1016/s0304-3975(03)00093-8","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0304-3975(03)00093-8","pdf_url":null,"source":{"id":"https://openalex.org/S90727058","display_name":"Theoretical Computer Science","issn_l":"0304-3975","issn":["0304-3975","1879-2294"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theoretical Computer Science","raw_type":"journal-article"},{"id":"pmh:oai:jah.su:record/273396","is_oa":false,"landing_page_url":"http://www.scopus.com/inward/record.url?partnerID=8YFLogxK&scp=0043238007","pdf_url":null,"source":{"id":"https://openalex.org/S4306401523","display_name":"Electronic scientific archive of UrFU (Ural Federal University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I130823665","host_organization_name":"Ural Federal University","host_organization_lineage":["https://openalex.org/I130823665"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theoretical Computer Science","raw_type":"Article"},{"id":"pmh:oai:elar.urfu.ru:10995/72275","is_oa":false,"landing_page_url":"http://www.scopus.com/inward/record.url?partnerID=8YFLogxK&scp=0043238007","pdf_url":null,"source":{"id":"https://openalex.org/S4306401522","display_name":"Electronic scientific archive of UrFU (Ural Federal University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I130823665","host_organization_name":"Ural Federal University","host_organization_lineage":["https://openalex.org/I130823665"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Theoretical Computer Science","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:re.public.polimi.it:11311/556325","is_oa":false,"landing_page_url":"http://hdl.handle.net/11311/556325","pdf_url":null,"source":{"id":"https://openalex.org/S4306400312","display_name":"Virtual Community of Pathological Anatomy (University of Castilla La Mancha)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79189158","host_organization_name":"University of Castilla-La Mancha","host_organization_lineage":["https://openalex.org/I79189158"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.6000000238418579,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320321873","display_name":"Ministero dell\u2019Istruzione, dell\u2019Universit\u00e0 e della Ricerca","ror":"https://ror.org/0166hxq48"},{"id":"https://openalex.org/F4320322515","display_name":"Saint Petersburg State University","ror":"https://ror.org/023znxa73"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W117573294","https://openalex.org/W1514300176","https://openalex.org/W1516116134","https://openalex.org/W1988082809","https://openalex.org/W1992850142","https://openalex.org/W2153126460","https://openalex.org/W2153632678","https://openalex.org/W2325110332","https://openalex.org/W2325416986","https://openalex.org/W2404463469","https://openalex.org/W2741608792","https://openalex.org/W6604788969","https://openalex.org/W6630675314","https://openalex.org/W6742759753"],"related_works":["https://openalex.org/W3099096946","https://openalex.org/W2016662589","https://openalex.org/W2159989507","https://openalex.org/W2021976774","https://openalex.org/W2361761646","https://openalex.org/W1507147345","https://openalex.org/W4300555302","https://openalex.org/W4300059198","https://openalex.org/W2952670229","https://openalex.org/W2132071306"],"abstract_inverted_index":null,"counts_by_year":[{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}