{"id":"https://openalex.org/W2041151288","doi":"https://doi.org/10.1142/s0218196708004822","title":"ON A GENERALIZATION OF DEHN'S ALGORITHM","display_name":"ON A GENERALIZATION OF DEHN'S ALGORITHM","publication_year":2008,"publication_date":"2008-11-01","ids":{"openalex":"https://openalex.org/W2041151288","doi":"https://doi.org/10.1142/s0218196708004822","mag":"2041151288","pmid":"https://pubmed.ncbi.nlm.nih.gov/20011460"},"language":"en","primary_location":{"id":"doi:10.1142/s0218196708004822","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196708004822","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","pubmed"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/2791467","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5062661455","display_name":"Oliver Goodman","orcid":null},"institutions":[{"id":"https://openalex.org/I165779595","display_name":"University of Melbourne","ror":"https://ror.org/01ej9dk98","country_code":"AU","type":"education","lineage":["https://openalex.org/I165779595"]}],"countries":["AU"],"is_corresponding":true,"raw_author_name":"OLIVER GOODMAN","raw_affiliation_strings":["Department of Mathematics and Statistics, University of Melbourne, Parkville, Victoria 3052, Australia"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Melbourne, Parkville, Victoria 3052, Australia","institution_ids":["https://openalex.org/I165779595"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5034173596","display_name":"Michael Shapiro","orcid":"https://orcid.org/0000-0002-2769-9320"},"institutions":[{"id":"https://openalex.org/I121934306","display_name":"Tufts University","ror":"https://ror.org/05wvpxv85","country_code":"US","type":"education","lineage":["https://openalex.org/I121934306"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"MICHAEL SHAPIRO","raw_affiliation_strings":["Department of Pathology, Tufts University, Boston, MA 02111, USA","Michael Shapiro wishes to thank David Thorley-Lawson for support from Public Health Service grant (RO1 AI062989). Additional support for this work came from NIH grant 1K25AI079404-01"],"affiliations":[{"raw_affiliation_string":"Department of Pathology, Tufts University, Boston, MA 02111, USA","institution_ids":["https://openalex.org/I121934306"]},{"raw_affiliation_string":"Michael Shapiro wishes to thank David Thorley-Lawson for support from Public Health Service grant (RO1 AI062989). Additional support for this work came from NIH grant 1K25AI079404-01","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5062661455"],"corresponding_institution_ids":["https://openalex.org/I165779595"],"apc_list":null,"apc_paid":null,"fwci":2.7263,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.89157216,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"18","issue":"07","first_page":"1137","last_page":"1177"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10304","display_name":"Geometric and Algebraic Topology","score":0.9998999834060669,"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":0.9998999834060669,"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/T11567","display_name":"semigroups and automata theory","score":0.9983999729156494,"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/T10849","display_name":"Finite Group Theory Research","score":0.9523000121116638,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8868674039840698},{"id":"https://openalex.org/keywords/word-problem","display_name":"Word problem (mathematics education)","score":0.7035329341888428},{"id":"https://openalex.org/keywords/nilpotent","display_name":"Nilpotent","score":0.6400247812271118},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.6181739568710327},{"id":"https://openalex.org/keywords/stallings-theorem-about-ends-of-groups","display_name":"Stallings theorem about ends of groups","score":0.6021536588668823},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.5382738709449768},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.527369499206543},{"id":"https://openalex.org/keywords/alphabet","display_name":"Alphabet","score":0.5136017799377441},{"id":"https://openalex.org/keywords/closure","display_name":"Closure (psychology)","score":0.5056638717651367},{"id":"https://openalex.org/keywords/generating-set-of-a-group","display_name":"Generating set of a group","score":0.46765488386154175},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4583835005760193},{"id":"https://openalex.org/keywords/nilpotent-group","display_name":"Nilpotent group","score":0.4573599100112915},{"id":"https://openalex.org/keywords/rewriting","display_name":"Rewriting","score":0.4485607147216797},{"id":"https://openalex.org/keywords/word","display_name":"Word (group theory)","score":0.4183214008808136},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.35884004831314087},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3584173321723938},{"id":"https://openalex.org/keywords/finitely-generated-abelian-group","display_name":"Finitely-generated abelian group","score":0.33018746972084045},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.18510374426841736},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10900053381919861},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.07726418972015381}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8868674039840698},{"id":"https://openalex.org/C90988201","wikidata":"https://www.wikidata.org/wiki/Q255912","display_name":"Word problem (mathematics education)","level":2,"score":0.7035329341888428},{"id":"https://openalex.org/C50555996","wikidata":"https://www.wikidata.org/wiki/Q840023","display_name":"Nilpotent","level":2,"score":0.6400247812271118},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.6181739568710327},{"id":"https://openalex.org/C58249144","wikidata":"https://www.wikidata.org/wiki/Q7597316","display_name":"Stallings theorem about ends of groups","level":3,"score":0.6021536588668823},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.5382738709449768},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.527369499206543},{"id":"https://openalex.org/C112876837","wikidata":"https://www.wikidata.org/wiki/Q837518","display_name":"Alphabet","level":2,"score":0.5136017799377441},{"id":"https://openalex.org/C146834321","wikidata":"https://www.wikidata.org/wiki/Q2979672","display_name":"Closure (psychology)","level":2,"score":0.5056638717651367},{"id":"https://openalex.org/C18116961","wikidata":"https://www.wikidata.org/wiki/Q734209","display_name":"Generating set of a group","level":2,"score":0.46765488386154175},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4583835005760193},{"id":"https://openalex.org/C206219070","wikidata":"https://www.wikidata.org/wiki/Q1755242","display_name":"Nilpotent group","level":3,"score":0.4573599100112915},{"id":"https://openalex.org/C154690210","wikidata":"https://www.wikidata.org/wiki/Q1668499","display_name":"Rewriting","level":2,"score":0.4485607147216797},{"id":"https://openalex.org/C90805587","wikidata":"https://www.wikidata.org/wiki/Q10944557","display_name":"Word (group theory)","level":2,"score":0.4183214008808136},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.35884004831314087},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3584173321723938},{"id":"https://openalex.org/C162860070","wikidata":"https://www.wikidata.org/wiki/Q142140","display_name":"Finitely-generated abelian group","level":2,"score":0.33018746972084045},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.18510374426841736},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10900053381919861},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07726418972015381},{"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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C34447519","wikidata":"https://www.wikidata.org/wiki/Q179522","display_name":"Market economy","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","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":6,"locations":[{"id":"doi:10.1142/s0218196708004822","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196708004822","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":"pmid:20011460","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/20011460","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International journal of algebra and computation","raw_type":null},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.250.6309","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.250.6309","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/0706.3024v3.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.251.1419","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.251.1419","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/0706.3024v2.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.251.1868","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.251.1868","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/0706.3024v4.pdf","raw_type":"text"},{"id":"pmh:oai:pubmedcentral.nih.gov:2791467","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/2791467","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Int J Algebra Comput","raw_type":"Text"}],"best_oa_location":{"id":"pmh:oai:pubmedcentral.nih.gov:2791467","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/2791467","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Int J Algebra Comput","raw_type":"Text"},"sustainable_development_goals":[{"score":0.6200000047683716,"id":"https://metadata.un.org/sdg/4","display_name":"Quality Education"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W28957298","https://openalex.org/W95736312","https://openalex.org/W611098039","https://openalex.org/W1578111061","https://openalex.org/W1972468537","https://openalex.org/W1975757718","https://openalex.org/W1977589901","https://openalex.org/W1981155305","https://openalex.org/W1984896712","https://openalex.org/W1995352162","https://openalex.org/W2002089154","https://openalex.org/W2028978432","https://openalex.org/W2032868343","https://openalex.org/W2038781886","https://openalex.org/W2045449896","https://openalex.org/W2065701704","https://openalex.org/W2068638265","https://openalex.org/W2087184562","https://openalex.org/W2103969576","https://openalex.org/W2131709870","https://openalex.org/W2158684550","https://openalex.org/W2963196760","https://openalex.org/W3102255413","https://openalex.org/W3104860897","https://openalex.org/W4248294038","https://openalex.org/W4302339081"],"related_works":["https://openalex.org/W1590360997","https://openalex.org/W2121545907","https://openalex.org/W2963589163","https://openalex.org/W1971568976","https://openalex.org/W2100417046","https://openalex.org/W2263979563","https://openalex.org/W2043951808","https://openalex.org/W4231260714","https://openalex.org/W1613949637","https://openalex.org/W1996018185"],"abstract_inverted_index":{"Viewing":[0],"Dehn's":[1],"algorithm":[2,31],"as":[3],"a":[4,70],"rewriting":[5],"system,":[6],"we":[7],"generalize":[8],"to":[9,36],"allow":[10],"an":[11,73,90],"alphabet":[12],"containing":[13],"letters":[14],"which":[15,29],"do":[16],"not":[17,87],"necessarily":[18],"represent":[19],"group":[20,71],"elements.":[21],"This":[22],"extends":[23],"the":[24,30,33],"class":[25,59],"of":[26,53,78],"groups":[27,45,49,52],"for":[28],"solves":[32],"word":[34],"problem":[35],"include":[37],"finitely":[38],"generated":[39],"nilpotent":[40],"groups,":[41],"many":[42],"relatively":[43],"hyperbolic":[44],"including":[46],"geometrically":[47,55],"finite":[48],"and":[50,76,81],"fundamental":[51],"certain":[54],"decomposable":[56],"3-manifolds.":[57],"The":[58],"has":[60,72],"several":[61],"nice":[62],"closure":[63],"properties.":[64],"We":[65,92],"also":[66],"show":[67],"that":[68],"if":[69],"infinite":[74],"subgroup":[75],"one":[77],"exponential":[79],"growth,":[80],"they":[82],"commute,":[83],"then":[84],"it":[85],"does":[86],"admit":[88],"such":[89],"algorithm.":[91],"dub":[93],"these":[94],"Cannon's":[95],"algorithms.":[96]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}