{"id":"https://openalex.org/W4386721941","doi":"https://doi.org/10.1215/00127094-2025-0055","title":"Hyperbolic groups satisfy the Boone\u2013Higman conjecture","display_name":"Hyperbolic groups satisfy the Boone\u2013Higman conjecture","publication_year":2026,"publication_date":"2026-05-14","ids":{"openalex":"https://openalex.org/W4386721941","doi":"https://doi.org/10.1215/00127094-2025-0055"},"language":"en","primary_location":{"id":"doi:10.1215/00127094-2025-0055","doi":"https://doi.org/10.1215/00127094-2025-0055","is_oa":false,"landing_page_url":"https://doi.org/10.1215/00127094-2025-0055","pdf_url":null,"source":{"id":"https://openalex.org/S171170845","display_name":"Duke Mathematical Journal","issn_l":"0012-7094","issn":["0012-7094","1547-7398"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-a","jufo-3","norway-2","poland-200","russia-white-list-1"],"host_organization":"https://openalex.org/P4310315698","host_organization_name":"Duke University Press","host_organization_lineage":["https://openalex.org/P4310315698","https://openalex.org/P4310315572"],"host_organization_lineage_names":["Duke University Press","Duke University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Duke Mathematical Journal","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2309.06224","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5066521656","display_name":"James Belk","orcid":"https://orcid.org/0000-0002-9392-3378","observed_orcids":["https://orcid.org/0000-0002-9392-3378"]},"institutions":[{"id":"https://openalex.org/I7882870","display_name":"University of Glasgow","ror":"https://ror.org/00vtgdb53","country_code":"GB","type":"education","lineage":["https://openalex.org/I7882870"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"James Belk","raw_affiliation_strings":["University of Glasgow, Glasgow, Scotland jim.belk@glasgow.ac.uk"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Glasgow, Glasgow, Scotland jim.belk@glasgow.ac.uk","institution_ids":["https://openalex.org/I7882870"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5064456055","display_name":"Collin Bleak","orcid":"https://orcid.org/0000-0001-5790-1940","observed_orcids":["https://orcid.org/0000-0001-5790-1940"]},"institutions":[{"id":"https://openalex.org/I16835326","display_name":"University of St Andrews","ror":"https://ror.org/02wn5qz54","country_code":"GB","type":"education","lineage":["https://openalex.org/I16835326"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Collin Bleak","raw_affiliation_strings":["University of St Andrews, St Andrews, Scotland collin.bleak@st-andrews.ac.uk"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of St Andrews, St Andrews, Scotland collin.bleak@st-andrews.ac.uk","institution_ids":["https://openalex.org/I16835326"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5042439079","display_name":"Francesco Matucci","orcid":"https://orcid.org/0000-0003-4762-5684","observed_orcids":["https://orcid.org/0000-0003-4762-5684"]},"institutions":[{"id":"https://openalex.org/I66752286","display_name":"University of Milano-Bicocca","ror":"https://ror.org/01ynf4891","country_code":"IT","type":"education","lineage":["https://openalex.org/I66752286"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Francesco Matucci","raw_affiliation_strings":["Universit\u00e0 di Milano\u2013Bicocca, Milan, Italy francesco.matucci@unimib.it"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00e0 di Milano\u2013Bicocca, Milan, Italy francesco.matucci@unimib.it","institution_ids":["https://openalex.org/I66752286"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5019208275","display_name":"Matthew C. B. Zaremsky","orcid":"https://orcid.org/0000-0003-2993-5777","observed_orcids":["https://orcid.org/0000-0003-2993-5777"]},"institutions":[{"id":"https://openalex.org/I1327163397","display_name":"State University of New York","ror":"https://ror.org/01q1z8k08","country_code":"US","type":"education","lineage":["https://openalex.org/I1327163397"]},{"id":"https://openalex.org/I392282","display_name":"University at Albany, State University of New York","ror":"https://ror.org/012zs8222","country_code":"US","type":"education","lineage":["https://openalex.org/I392282"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Matthew C. B. Zaremsky","raw_affiliation_strings":["Department of Mathematics and Statistics, University at Albany, State University of New York, Albany, New York, USA mzaremsky@albany.edu"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, University at Albany, State University of New York, Albany, New York, USA mzaremsky@albany.edu","institution_ids":["https://openalex.org/I1327163397","https://openalex.org/I392282"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":16.118,"has_fulltext":true,"cited_by_count":20,"citation_normalized_percentile":{"value":0.99374857,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":88,"max":99},"biblio":{"volume":"175","issue":"9","first_page":"1519","last_page":"1592"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10304","display_name":"Geometric and Algebraic Topology","score":0.9878000020980835,"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":0.9878000020980835,"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/T10849","display_name":"Finite Group Theory Research","score":0.004100000020116568,"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/T12504","display_name":"Mathematics and Applications","score":0.0008999999845400453,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/hyperbolic-groups","display_name":"hyperbolic groups","score":0.9990000128746033},{"id":"https://openalex.org/keywords/solvable-word-problem","display_name":"solvable word problem","score":0.8370000123977661},{"id":"https://openalex.org/keywords/group-embeddings","display_name":"group embeddings","score":0.5540000200271606},{"id":"https://openalex.org/keywords/self-similar-groups","display_name":"self-similar groups","score":0.8539999723434448},{"id":"https://openalex.org/keywords/finitely-generated-groups","display_name":"finitely generated groups","score":0.7900000214576721}],"concepts":[{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.8300377130508423},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7849311828613281},{"id":"https://openalex.org/C162860070","wikidata":"https://www.wikidata.org/wiki/Q142140","display_name":"Finitely-generated abelian group","level":2,"score":0.631888747215271},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.6315519213676453},{"id":"https://openalex.org/C5383885","wikidata":"https://www.wikidata.org/wiki/Q571124","display_name":"Simple group","level":3,"score":0.5998255610466003},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.555877685546875},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.47284701466560364},{"id":"https://openalex.org/C167150821","wikidata":"https://www.wikidata.org/wiki/Q81194","display_name":"Hyperbolic group","level":4,"score":0.44199827313423157},{"id":"https://openalex.org/C40020168","wikidata":"https://www.wikidata.org/wiki/Q7310818","display_name":"Relatively hyperbolic group","level":4,"score":0.4337081015110016},{"id":"https://openalex.org/C90988201","wikidata":"https://www.wikidata.org/wiki/Q255912","display_name":"Word problem (mathematics education)","level":2,"score":0.41805899143218994},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.40197479724884033},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.39574748277664185},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.16200315952301025},{"id":"https://openalex.org/C70984080","wikidata":"https://www.wikidata.org/wiki/Q2619102","display_name":"Hyperbolic manifold","level":3,"score":0.15351051092147827},{"id":"https://openalex.org/C92047909","wikidata":"https://www.wikidata.org/wiki/Q204034","display_name":"Hyperbolic function","level":2,"score":0.07027450203895569},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07018965482711792},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","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/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1215/00127094-2025-0055","doi":"https://doi.org/10.1215/00127094-2025-0055","is_oa":false,"landing_page_url":"https://doi.org/10.1215/00127094-2025-0055","pdf_url":null,"source":{"id":"https://openalex.org/S171170845","display_name":"Duke Mathematical Journal","issn_l":"0012-7094","issn":["0012-7094","1547-7398"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-a","jufo-3","norway-2","poland-200","russia-white-list-1"],"host_organization":"https://openalex.org/P4310315698","host_organization_name":"Duke University Press","host_organization_lineage":["https://openalex.org/P4310315698","https://openalex.org/P4310315572"],"host_organization_lineage_names":["Duke University Press","Duke University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Duke Mathematical Journal","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2309.06224","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2309.06224","pdf_url":"https://arxiv.org/pdf/2309.06224","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:eprints.gla.ac.uk:363942","doi":null,"is_oa":true,"landing_page_url":"https://eprints.gla.ac.uk/view/author/67712.html>","pdf_url":"https://eprints.gla.ac.uk/363942/3/363942.pdf","source":{"id":"https://openalex.org/S4210235606","display_name":"ENLIGHTEN (Jurnal Bimbingan dan Konseling Islam)","issn_l":"2622-8912","issn":["2622-8912","2622-8920"],"is_oa":true,"is_in_doaj":true,"is_core":false,"listed_in":["doaj"],"host_organization":"https://openalex.org/I4405259220","host_organization_name":"Institut Agama Islam Negeri Langsa","host_organization_lineage":["https://openalex.org/I4405259220"],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Articles"},{"id":"pmh:oai:boa.unimib.it:10281/605841","doi":null,"is_oa":true,"landing_page_url":"https://hdl.handle.net/10281/605841","pdf_url":null,"source":{"id":"https://openalex.org/S4306401259","display_name":"BOA (University of Milano-Bicocca)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I66752286","host_organization_name":"University of Milano-Bicocca","host_organization_lineage":["https://openalex.org/I66752286"],"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":null,"raw_type":"info:eu-repo/semantics/article"},{"id":"doi:10.48550/arxiv.2309.06224","doi":"https://doi.org/10.48550/arxiv.2309.06224","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2309.06224","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2309.06224","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2309.06224","pdf_url":"https://arxiv.org/pdf/2309.06224","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320320337","display_name":"University of Glasgow","ror":"https://ror.org/00vtgdb53"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4386721941.pdf","grobid_xml":"https://content.openalex.org/works/W4386721941.grobid-xml"},"referenced_works_count":57,"referenced_works":["https://openalex.org/W417925666","https://openalex.org/W1490263025","https://openalex.org/W1551901108","https://openalex.org/W1565611252","https://openalex.org/W1706415889","https://openalex.org/W1834284857","https://openalex.org/W1967684312","https://openalex.org/W1971435636","https://openalex.org/W1977665851","https://openalex.org/W2000270556","https://openalex.org/W2010414076","https://openalex.org/W2019271765","https://openalex.org/W2025265575","https://openalex.org/W2028978432","https://openalex.org/W2032995160","https://openalex.org/W2061890881","https://openalex.org/W2065145870","https://openalex.org/W2068258253","https://openalex.org/W2070866382","https://openalex.org/W2073723685","https://openalex.org/W2078103151","https://openalex.org/W2080468319","https://openalex.org/W2091151350","https://openalex.org/W2091797401","https://openalex.org/W2092485069","https://openalex.org/W2112468359","https://openalex.org/W2130420929","https://openalex.org/W2134086356","https://openalex.org/W2156107686","https://openalex.org/W2185602163","https://openalex.org/W2295375514","https://openalex.org/W2526438477","https://openalex.org/W2763619959","https://openalex.org/W2765538030","https://openalex.org/W2767468241","https://openalex.org/W2770924688","https://openalex.org/W2774308779","https://openalex.org/W2807516619","https://openalex.org/W2963950238","https://openalex.org/W2964342717","https://openalex.org/W2998896789","https://openalex.org/W3011921575","https://openalex.org/W3048735228","https://openalex.org/W3095447068","https://openalex.org/W3152775830","https://openalex.org/W3176467405","https://openalex.org/W4226338790","https://openalex.org/W4235484205","https://openalex.org/W4240368649","https://openalex.org/W4248991867","https://openalex.org/W4313435838","https://openalex.org/W4327991779","https://openalex.org/W4382334275","https://openalex.org/W4387225924","https://openalex.org/W4399781848","https://openalex.org/W4402744960","https://openalex.org/W4411351207"],"related_works":["https://openalex.org/W4382334275","https://openalex.org/W7037303863","https://openalex.org/W4407450664","https://openalex.org/W4411351207","https://openalex.org/W4411067427","https://openalex.org/W2770924688","https://openalex.org/W7221532280","https://openalex.org/W4416419596","https://openalex.org/W1831118846","https://openalex.org/W2013455429"],"abstract_inverted_index":{"The":[0],"1973":[1],"Boone\u2013Higman":[2,122],"conjecture":[3,48],"predicts":[4],"that":[5,26,32,46,74,83,115],"every":[6,84,94],"finitely":[7,17,40,55,101],"generated":[8],"group":[9,36,86],"with":[10],"solvable":[11],"word":[12],"problem":[13],"embeds":[14,37,87,98],"in":[15,38,50,77,88,99],"a":[16,62,89,100],"presented":[18,41,56,102],"simple":[19,42,103],"group.":[20,43],"In":[21],"this":[22,30],"paper,":[23],"we":[24,68],"show":[25],"hyperbolic":[27,35,85],"groups":[28,72,119],"satisfy":[29,120],"conjecture,":[31],"is,":[33],"each":[34],"some":[39],"This":[44],"shows":[45],"the":[47,51,107,121],"holds":[49],"\u201cgeneric\u201d":[52],"case":[53],"for":[54],"groups.":[57],"Our":[58],"key":[59],"tool":[60],"is":[61,75,114],"new":[63],"family":[64],"of":[65,111],"groups,":[66],"which":[67],"call":[69],"rational":[70],"similarity":[71],"(RSGs),":[73],"interesting":[76],"its":[78],"own":[79],"right.":[80],"We":[81],"prove":[82],"full,":[90,95],"contracting":[91,96,117],"RSG,":[92],"and":[93],"RSG":[97],"group,":[104],"thus":[105],"establishing":[106],"result.":[108],"Another":[109],"consequence":[110],"our":[112],"work":[113],"all":[116],"self-similar":[118],"conjecture.":[123]},"counts_by_year":[{"year":2026,"cited_by_count":8},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2023-09-14T00:00:00"}