{"id":"https://openalex.org/W2563956635","doi":"https://doi.org/10.1142/s0218196718500054","title":"On Andrews\u2013Curtis conjectures for soluble groups","display_name":"On Andrews\u2013Curtis conjectures for soluble groups","publication_year":2017,"publication_date":"2017-12-06","ids":{"openalex":"https://openalex.org/W2563956635","doi":"https://doi.org/10.1142/s0218196718500054","mag":"2563956635"},"language":"en","primary_location":{"id":"doi:10.1142/s0218196718500054","is_oa":true,"landing_page_url":"https://doi.org/10.1142/s0218196718500054","pdf_url":"https://www.worldscientific.com/doi/pdf/10.1142/S0218196718500054","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":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.worldscientific.com/doi/pdf/10.1142/S0218196718500054","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5004647418","display_name":"Luc Guyot","orcid":"https://orcid.org/0000-0003-1533-8226"},"institutions":[{"id":"https://openalex.org/I5124864","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I5124864"]}],"countries":["CH"],"is_corresponding":true,"raw_author_name":"Luc Guyot","raw_affiliation_strings":["EPFL ENT CBS BBP/HBP. Campus Biotech. B1 Building, Chemin des Mines, 9, Geneva 1202, Switzerland"],"affiliations":[{"raw_affiliation_string":"EPFL ENT CBS BBP/HBP. Campus Biotech. B1 Building, Chemin des Mines, 9, Geneva 1202, Switzerland","institution_ids":["https://openalex.org/I5124864"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5004647418"],"corresponding_institution_ids":["https://openalex.org/I5124864"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.06807984,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"28","issue":"01","first_page":"97","last_page":"113"},"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/T10899","display_name":"Advanced Operator Algebra Research","score":0.9977999925613403,"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/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.9962999820709229,"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/conjecture","display_name":"Conjecture","score":0.8776905536651611},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8355069160461426},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7364538908004761},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.65159672498703},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.6364850997924805},{"id":"https://openalex.org/keywords/free-group","display_name":"Free group","score":0.46325454115867615},{"id":"https://openalex.org/keywords/finitely-generated-abelian-group","display_name":"Finitely-generated abelian group","score":0.4370431900024414},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3216175138950348}],"concepts":[{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.8776905536651611},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8355069160461426},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7364538908004761},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.65159672498703},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.6364850997924805},{"id":"https://openalex.org/C77021192","wikidata":"https://www.wikidata.org/wiki/Q431078","display_name":"Free group","level":3,"score":0.46325454115867615},{"id":"https://openalex.org/C162860070","wikidata":"https://www.wikidata.org/wiki/Q142140","display_name":"Finitely-generated abelian group","level":2,"score":0.4370431900024414},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3216175138950348},{"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}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1142/s0218196718500054","is_oa":true,"landing_page_url":"https://doi.org/10.1142/s0218196718500054","pdf_url":"https://www.worldscientific.com/doi/pdf/10.1142/S0218196718500054","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":"pmh:oai:arXiv.org:1612.06912","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1612.06912","pdf_url":"https://arxiv.org/pdf/1612.06912","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":"","raw_type":"text"},{"id":"mag:2563956635","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1612.06912","pdf_url":null,"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":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:infoscience.epfl.ch:259548","is_oa":true,"landing_page_url":"http://infoscience.epfl.ch/record/259548","pdf_url":null,"source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://infoscience.epfl.ch/record/259548","raw_type":"Text"},{"id":"doi:10.48550/arxiv.1612.06912","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1612.06912","pdf_url":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.1142/s0218196718500054","is_oa":true,"landing_page_url":"https://doi.org/10.1142/s0218196718500054","pdf_url":"https://www.worldscientific.com/doi/pdf/10.1142/S0218196718500054","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"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2563956635.pdf","grobid_xml":"https://content.openalex.org/works/W2563956635.grobid-xml"},"referenced_works_count":31,"referenced_works":["https://openalex.org/W22673372","https://openalex.org/W152400436","https://openalex.org/W1516116134","https://openalex.org/W1570168301","https://openalex.org/W1579941411","https://openalex.org/W1849413508","https://openalex.org/W1971506185","https://openalex.org/W1978700303","https://openalex.org/W1991400804","https://openalex.org/W2015894047","https://openalex.org/W2026468639","https://openalex.org/W2053384159","https://openalex.org/W2055356126","https://openalex.org/W2057361225","https://openalex.org/W2064867304","https://openalex.org/W2065772166","https://openalex.org/W2072937648","https://openalex.org/W2089978351","https://openalex.org/W2122560542","https://openalex.org/W2225205306","https://openalex.org/W2264050275","https://openalex.org/W2313812001","https://openalex.org/W2323948755","https://openalex.org/W2592593424","https://openalex.org/W2963083310","https://openalex.org/W2963901754","https://openalex.org/W3021045634","https://openalex.org/W3102726613","https://openalex.org/W3103780995","https://openalex.org/W4239749567","https://openalex.org/W4292101339"],"related_works":["https://openalex.org/W2963060928","https://openalex.org/W2953384431","https://openalex.org/W2011926017","https://openalex.org/W1484135350","https://openalex.org/W2950313263","https://openalex.org/W2097580841","https://openalex.org/W3102259815","https://openalex.org/W2041673132","https://openalex.org/W3014552430","https://openalex.org/W2123387752","https://openalex.org/W1997112733","https://openalex.org/W3098788264","https://openalex.org/W2359293412","https://openalex.org/W3124709744","https://openalex.org/W1985585355","https://openalex.org/W3185610785","https://openalex.org/W2899500736","https://openalex.org/W1996530961","https://openalex.org/W2293412965","https://openalex.org/W3081460691"],"abstract_inverted_index":{"The":[0],"Andrews\u2013Curtis":[1,71,95],"conjecture":[2,72,96],"claims":[3],"that":[4,62,85],"every":[5,63],"normally":[6],"generating":[7],"[Formula:":[8,15,20,38],"see":[9,16,21,39],"text]-tuple":[10],"of":[11,18,31,76,100],"a":[12,27],"free":[13],"group":[14,46,67],"text]":[17,22,40],"rank":[19],"can":[23],"be":[24],"reduced":[25],"to":[26],"basis":[28],"by":[29,41],"means":[30],"Nielsen":[32],"transformations":[33],"and":[34,57,79,102],"arbitrary":[35,43],"conjugations.":[36],"Replacing":[37],"an":[42],"finitely":[44,64],"generated":[45,65],"yields":[47],"natural":[48],"generalizations":[49],"whose":[50],"study":[51],"may":[52],"help":[53],"disprove":[54],"the":[55,69,74,93,98],"original":[56],"unsettled":[58],"conjecture.":[59],"We":[60],"prove":[61],"soluble":[66,87],"satisfies":[68],"generalized":[70,94],"in":[73,97],"sense":[75,99],"Borovik,":[77],"Lubotzky":[78],"Myasnikov.":[80],"In":[81],"contrast,":[82],"we":[83],"show":[84],"some":[86],"Baumslag\u2013Solitar":[88],"groups":[89],"do":[90],"not":[91],"satisfy":[92],"Burns":[101],"Macedo\u0144ska.":[103]},"counts_by_year":[],"updated_date":"2026-02-09T09:26:11.010843","created_date":"2025-10-10T00:00:00"}