{"id":"https://openalex.org/W2146436017","doi":"https://doi.org/10.1112/jlms/jdu009","title":"Growth of primitive elements in free groups","display_name":"Growth of primitive elements in free groups","publication_year":2014,"publication_date":"2014-05-20","ids":{"openalex":"https://openalex.org/W2146436017","doi":"https://doi.org/10.1112/jlms/jdu009","mag":"2146436017"},"language":"en","primary_location":{"id":"doi:10.1112/jlms/jdu009","is_oa":false,"landing_page_url":"https://doi.org/10.1112/jlms/jdu009","pdf_url":null,"source":{"id":"https://openalex.org/S4210207695","display_name":"Journal of the London Mathematical Society","issn_l":"0024-6107","issn":["0024-6107","1469-7750"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of the London Mathematical Society","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1304.7979","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"D. Puder","orcid":null},"institutions":[{"id":"https://openalex.org/I197251160","display_name":"Hebrew University of Jerusalem","ror":"https://ror.org/03qxff017","country_code":"IL","type":"education","lineage":["https://openalex.org/I197251160"]}],"countries":["IL"],"is_corresponding":true,"raw_author_name":"D. Puder","raw_affiliation_strings":["Einstein Institute of Mathematics, Edmond J. Safra Campus, Givat Ram, The Hebrew University of Jerusalem, Jerusalem 91904, Israel"],"affiliations":[{"raw_affiliation_string":"Einstein Institute of Mathematics, Edmond J. Safra Campus, Givat Ram, The Hebrew University of Jerusalem, Jerusalem 91904, Israel","institution_ids":["https://openalex.org/I197251160"]}]},{"author_position":"last","author":{"id":null,"display_name":"C. Wu","orcid":null},"institutions":[{"id":"https://openalex.org/I20089843","display_name":"Princeton University","ror":"https://ror.org/00hx57361","country_code":"US","type":"education","lineage":["https://openalex.org/I20089843"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"C. Wu","raw_affiliation_strings":["Department of Mathematics, Princeton University, Fine Hall, Washington Road, Princeton, NJ 08544-1000, USA, [email protected]"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Princeton University, Fine Hall, Washington Road, Princeton, NJ 08544-1000, USA, [email protected]","institution_ids":["https://openalex.org/I20089843"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I197251160"],"apc_list":{"value":3710,"currency":"USD","value_usd":3710},"apc_paid":null,"fwci":1.8727,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.85183468,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"90","issue":"1","first_page":"89","last_page":"104"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10304","display_name":"Geometric and Algebraic Topology","score":0.2476000040769577,"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":0.2476000040769577,"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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.23890000581741333,"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"}},{"id":"https://openalex.org/T10899","display_name":"Advanced Operator Algebra Research","score":0.1128000020980835,"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/primitive-element","display_name":"Primitive element","score":0.7549999952316284},{"id":"https://openalex.org/keywords/element","display_name":"Element (criminal law)","score":0.5493999719619751},{"id":"https://openalex.org/keywords/word","display_name":"Word (group theory)","score":0.490200012922287},{"id":"https://openalex.org/keywords/free-group","display_name":"Free group","score":0.47530001401901245},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.44449999928474426},{"id":"https://openalex.org/keywords/primitive-polynomial","display_name":"Primitive polynomial","score":0.4244000017642975},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.4016999900341034}],"concepts":[{"id":"https://openalex.org/C144825994","wikidata":"https://www.wikidata.org/wiki/Q4378669","display_name":"Primitive element","level":3,"score":0.7549999952316284},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7261000275611877},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.645799994468689},{"id":"https://openalex.org/C200288055","wikidata":"https://www.wikidata.org/wiki/Q2621792","display_name":"Element (criminal law)","level":2,"score":0.5493999719619751},{"id":"https://openalex.org/C90805587","wikidata":"https://www.wikidata.org/wiki/Q10944557","display_name":"Word (group theory)","level":2,"score":0.490200012922287},{"id":"https://openalex.org/C77021192","wikidata":"https://www.wikidata.org/wiki/Q431078","display_name":"Free group","level":3,"score":0.47530001401901245},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.44449999928474426},{"id":"https://openalex.org/C41620472","wikidata":"https://www.wikidata.org/wiki/Q1458669","display_name":"Primitive polynomial","level":3,"score":0.4244000017642975},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.41190001368522644},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.4016999900341034},{"id":"https://openalex.org/C3019641298","wikidata":"https://www.wikidata.org/wiki/Q625642","display_name":"Word length","level":2,"score":0.36570000648498535},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.34040001034736633},{"id":"https://openalex.org/C75235859","wikidata":"https://www.wikidata.org/wiki/Q582659","display_name":"Exponential growth","level":2,"score":0.32109999656677246},{"id":"https://openalex.org/C47527751","wikidata":"https://www.wikidata.org/wiki/Q1454165","display_name":"Free product","level":3,"score":0.303600013256073},{"id":"https://openalex.org/C6026789","wikidata":"https://www.wikidata.org/wiki/Q948010","display_name":"Primitive root modulo n","level":3,"score":0.29499998688697815},{"id":"https://openalex.org/C2780388253","wikidata":"https://www.wikidata.org/wiki/Q5421508","display_name":"Exponent","level":2,"score":0.2615000009536743},{"id":"https://openalex.org/C184264201","wikidata":"https://www.wikidata.org/wiki/Q21199","display_name":"Natural number","level":2,"score":0.25760000944137573},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.25099998712539673}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1112/jlms/jdu009","is_oa":false,"landing_page_url":"https://doi.org/10.1112/jlms/jdu009","pdf_url":null,"source":{"id":"https://openalex.org/S4210207695","display_name":"Journal of the London Mathematical Society","issn_l":"0024-6107","issn":["0024-6107","1469-7750"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of the London Mathematical Society","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1304.7979","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1304.7979","pdf_url":"https://arxiv.org/pdf/1304.7979","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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1304.7979","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1304.7979","pdf_url":"https://arxiv.org/pdf/1304.7979","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W1538796668","https://openalex.org/W1967932087","https://openalex.org/W2007624900","https://openalex.org/W2019264400","https://openalex.org/W2040037490","https://openalex.org/W2076164649","https://openalex.org/W2315950575","https://openalex.org/W2504552467","https://openalex.org/W3010911246","https://openalex.org/W4236703290","https://openalex.org/W4253852412"],"related_works":[],"abstract_inverted_index":{"In":[0,22],"the":[1,50,81,101,122,127],"free":[2,19,136],"group":[3],"F":[4,90],"k":[5,77,91,97,107,112],",":[6,78,100,108],"an":[7],"element":[8,31],"is":[9,110],"said":[10],"to":[11,17,38,133],"be":[12,80],"primitive":[13,30,42,84],"if":[14],"it":[15],"belongs":[16],"a":[18,28,40,65,134],"generating":[20],"set.":[21],"this":[23],"paper,":[24],"we":[25],"describe":[26],"what":[27],"generic":[29],"looks":[32],"like.":[33],"We":[34,93],"prove":[35],"that":[36,95],"up":[37],"conjugation,":[39],"random":[41],"word":[43],"of":[44,49,83,86,105,126,130],"length":[45,87],"N":[46,58,79,88,109],"contains":[47],"one":[48],"letters":[51],"exactly":[52],"once":[53],"asymptotically":[54],"almost":[55],"surely":[56],"(as":[57],"\u2192":[59],"\u221e":[60],").":[61],"This":[62],"also":[63,118],"solves":[64],"question":[66],"raised":[67],"by":[68],"Baumslag\u2013Myasnikov\u2013Shpilrain":[69],"(Contemp.":[70],"Math.":[71],"296":[72],"(2002)":[73],"1\u201338).":[74],"Let":[75],"p":[76,106],"number":[82],"words":[85],"in":[89],".":[92,115],"show":[94],"for":[96,120],"\u2a7e":[98],"3":[99,114],"exponential":[102],"growth":[103,124],"rate":[104,125],"2":[111],"\u2212":[113],"Our":[116],"proof":[117],"works":[119],"giving":[121],"exact":[123],"larger":[128],"class":[129],"elements":[131],"belonging":[132],"proper":[135],"factor.":[137]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2014,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2016-06-24T00:00:00"}
