{"id":"https://openalex.org/W2090181075","doi":"https://doi.org/10.1142/s0218196706003013","title":"SOME EQUATIONS OVER TORSION-FREE GROUPS","display_name":"SOME EQUATIONS OVER TORSION-FREE GROUPS","publication_year":2006,"publication_date":"2006-04-01","ids":{"openalex":"https://openalex.org/W2090181075","doi":"https://doi.org/10.1142/s0218196706003013","mag":"2090181075"},"language":"en","primary_location":{"id":"doi:10.1142/s0218196706003013","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196706003013","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/A5088259382","display_name":"Seong Kun Kim","orcid":null},"institutions":[{"id":"https://openalex.org/I4921948","display_name":"Pusan National University","ror":"https://ror.org/01an57a31","country_code":"KR","type":"education","lineage":["https://openalex.org/I4921948"]}],"countries":["KR"],"is_corresponding":true,"raw_author_name":"SEONG KUN KIM","raw_affiliation_strings":["Department of Mathematics, Pusan National University, Pusan, South Korea 609-735, South Korea"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Pusan National University, Pusan, South Korea 609-735, South Korea","institution_ids":["https://openalex.org/I4921948"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5088259382"],"corresponding_institution_ids":["https://openalex.org/I4921948"],"apc_list":null,"apc_paid":null,"fwci":0.417,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.61119003,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"16","issue":"02","first_page":"369","last_page":"376"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10304","display_name":"Geometric and Algebraic Topology","score":0.9628999829292297,"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":0.9628999829292297,"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/T12508","display_name":"Functional Equations Stability Results","score":0.9028000235557556,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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":0.9071011543273926},{"id":"https://openalex.org/keywords/torsion","display_name":"Torsion (gastropod)","score":0.8100008964538574},{"id":"https://openalex.org/keywords/exponent","display_name":"Exponent","score":0.6796458959579468},{"id":"https://openalex.org/keywords/free-group","display_name":"Free group","score":0.5010025501251221},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4022570550441742},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.34893476963043213},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3481047749519348},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.22627565264701843},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.05668765306472778},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.04201468825340271}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9071011543273926},{"id":"https://openalex.org/C77461463","wikidata":"https://www.wikidata.org/wiki/Q7827201","display_name":"Torsion (gastropod)","level":2,"score":0.8100008964538574},{"id":"https://openalex.org/C2780388253","wikidata":"https://www.wikidata.org/wiki/Q5421508","display_name":"Exponent","level":2,"score":0.6796458959579468},{"id":"https://openalex.org/C77021192","wikidata":"https://www.wikidata.org/wiki/Q431078","display_name":"Free group","level":3,"score":0.5010025501251221},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4022570550441742},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.34893476963043213},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3481047749519348},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.22627565264701843},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.05668765306472778},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.04201468825340271},{"id":"https://openalex.org/C141071460","wikidata":"https://www.wikidata.org/wiki/Q40821","display_name":"Surgery","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},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218196706003013","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196706003013","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W569485294","https://openalex.org/W1837248567","https://openalex.org/W1974152966","https://openalex.org/W2017671777","https://openalex.org/W2036379756","https://openalex.org/W2057499020","https://openalex.org/W2067822611","https://openalex.org/W2098497745","https://openalex.org/W2155373620","https://openalex.org/W2316031802","https://openalex.org/W2488104763","https://openalex.org/W2506084698"],"related_works":["https://openalex.org/W2467119940","https://openalex.org/W3194077685","https://openalex.org/W2152758797","https://openalex.org/W2382762871","https://openalex.org/W2950599922","https://openalex.org/W2062219402","https://openalex.org/W4286787881","https://openalex.org/W2952238393","https://openalex.org/W2008992764","https://openalex.org/W1805197905"],"abstract_inverted_index":{"We":[0],"prove":[1],"that":[2,34],"equations":[3,43],"x":[4,9,15],"m":[5,10,16],"1":[6,8],"h":[7,12,18],"2":[11,13],"\u22ef":[14],"k":[17,19,26],"over":[20,48],"torsion-free":[21,49],"groups":[22],"are":[23],"solvable":[24],"when":[25],"\u2264":[27],"4.":[28],"In":[29],"the":[30,35],"conclusion,":[31],"we":[32],"assert":[33],"Levin":[36],"question":[37],"is":[38],"equivalent":[39],"to":[40],"solving":[41],"certain":[42],"with":[44],"exponent":[45],"sum":[46],"zero":[47],"groups.":[50]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
