{"id":"https://openalex.org/W4411988263","doi":"https://doi.org/10.46298/jgcc.2025..15972","title":"Andrews-Curtis groups","display_name":"Andrews-Curtis groups","publication_year":2025,"publication_date":"2025-07-04","ids":{"openalex":"https://openalex.org/W4411988263","doi":"https://doi.org/10.46298/jgcc.2025..15972"},"language":"en","primary_location":{"id":"doi:10.46298/jgcc.2025..15972","is_oa":true,"landing_page_url":"https://doi.org/10.46298/jgcc.2025..15972","pdf_url":"https://gcc.episciences.org/15972/pdf","source":{"id":"https://openalex.org/S4210228216","display_name":"journal of Groups complexity cryptology","issn_l":"1867-1144","issn":["1867-1144","1869-6104"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310321880","host_organization_name":"\u00c9pisciences.org","host_organization_lineage":["https://openalex.org/P4310321880"],"host_organization_lineage_names":["\u00c9pisciences.org"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"journal of Groups, complexity, cryptology","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://gcc.episciences.org/15972/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5040912618","display_name":"Robert H. Gilman","orcid":"https://orcid.org/0000-0002-9037-0712"},"institutions":[{"id":"https://openalex.org/I108468826","display_name":"Stevens Institute of Technology","ror":"https://ror.org/02z43xh36","country_code":"US","type":"education","lineage":["https://openalex.org/I108468826"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Robert H. Gilman","raw_affiliation_strings":["Stevens Institute of Technology"],"affiliations":[{"raw_affiliation_string":"Stevens Institute of Technology","institution_ids":["https://openalex.org/I108468826"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5112447861","display_name":"Alexei Myasnikov","orcid":null},"institutions":[{"id":"https://openalex.org/I108468826","display_name":"Stevens Institute of Technology","ror":"https://ror.org/02z43xh36","country_code":"US","type":"education","lineage":["https://openalex.org/I108468826"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Alexei G. Myasnikov","raw_affiliation_strings":["Stevens Institute of Technology"],"affiliations":[{"raw_affiliation_string":"Stevens Institute of Technology","institution_ids":["https://openalex.org/I108468826"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5040912618"],"corresponding_institution_ids":["https://openalex.org/I108468826"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.13808826,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"Volume 16, Issue 1, Special...","issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10911","display_name":"Chemical Synthesis and Analysis","score":0.9904000163078308,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},"topics":[{"id":"https://openalex.org/T10911","display_name":"Chemical Synthesis and Analysis","score":0.9904000163078308,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/geography","display_name":"Geography","score":0.3536721169948578}],"concepts":[{"id":"https://openalex.org/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","level":0,"score":0.3536721169948578}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.46298/jgcc.2025..15972","is_oa":true,"landing_page_url":"https://doi.org/10.46298/jgcc.2025..15972","pdf_url":"https://gcc.episciences.org/15972/pdf","source":{"id":"https://openalex.org/S4210228216","display_name":"journal of Groups complexity cryptology","issn_l":"1867-1144","issn":["1867-1144","1869-6104"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310321880","host_organization_name":"\u00c9pisciences.org","host_organization_lineage":["https://openalex.org/P4310321880"],"host_organization_lineage_names":["\u00c9pisciences.org"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"journal of Groups, complexity, cryptology","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2506.23031","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2506.23031","pdf_url":"https://arxiv.org/pdf/2506.23031","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"doi:10.46298/jgcc.2025..15972","is_oa":true,"landing_page_url":"https://doi.org/10.46298/jgcc.2025..15972","pdf_url":"https://gcc.episciences.org/15972/pdf","source":{"id":"https://openalex.org/S4210228216","display_name":"journal of Groups complexity cryptology","issn_l":"1867-1144","issn":["1867-1144","1869-6104"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310321880","host_organization_name":"\u00c9pisciences.org","host_organization_lineage":["https://openalex.org/P4310321880"],"host_organization_lineage_names":["\u00c9pisciences.org"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"journal of Groups, complexity, cryptology","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G73215019","display_name":null,"funder_award_id":"FR-21-4713","funder_id":"https://openalex.org/F4320322898","funder_display_name":"Shota Rustaveli National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320322898","display_name":"Shota Rustaveli National Science Foundation","ror":"https://ror.org/00xc87681"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4411988263.pdf","grobid_xml":"https://content.openalex.org/works/W4411988263.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W3120165752","https://openalex.org/W3158585187","https://openalex.org/W2344506138","https://openalex.org/W1964191721","https://openalex.org/W2485179383","https://openalex.org/W4211064241","https://openalex.org/W3195275078","https://openalex.org/W2073705106","https://openalex.org/W4237393413"],"abstract_inverted_index":{"For":[0],"any":[1],"group":[2,19,78],"$G$":[3,32,48,106],"and":[4],"integer":[5],"$k\\ge":[6],"2$":[7],"the":[8,17,22,75,95],"Andrews-Curtis":[9,18,43,77],"transformations":[10],"act":[11],"as":[12,33],"a":[13,34,65,84],"permutation":[14],"group,":[15],"termed":[16],"$AC_k(G)$,":[20],"on":[21,58,83,115],"subset":[23],"$N_k(G)":[24],"\\subset":[25],"G^k$":[26],"of":[27,51,119,133,139],"all":[28],"$k$-tuples":[29],"that":[30,46,104],"generate":[31],"normal":[35],"subgroup":[36],"(provided":[37],"$N_k(G)$":[38,62],"is":[39,45,49,71,92,107,126],"non-empty).":[40],"The":[41,60],"famous":[42],"Conjecture":[44],"if":[47,105],"free":[50],"rank":[52],"$k$,":[53],"then":[54,111],"$AC_k(G)$":[55],"acts":[56,113],"transitively":[57],"$N_k(G)$.":[59],"set":[61,87],"may":[63],"have":[64],"rather":[66],"complex":[67],"structure,":[68],"so":[69],"it":[70],"easier":[72],"to":[73,93],"study":[74],"full":[76],"$FAC(G)$":[79],"generated":[80],"by":[81],"AC-transformations":[82],"much":[85],"simpler":[86],"$G^k$.":[88],"Our":[89],"goal":[90],"here":[91],"investigate":[94],"natural":[96],"epimorphism":[97],"$\u03bb\\colon":[98,122],"FAC_k(G)":[99,123],"\\to":[100,124],"AC_k(G)$.":[101],"We":[102],"show":[103],"non-elementary":[108],"torsion-free":[109],"hyperbolic,":[110],"$FAC_k(G)$":[112],"faithfully":[114],"every":[116],"nontrivial":[117],"orbit":[118],"$G^k$,":[120],"hence":[121],"AC_k(G)$":[125],"an":[127],"isomorphism.":[128],"7":[129],"pages.":[130],"In":[131],"memory":[132],"Ben":[134],"Fine.":[135],"Published":[136],"in":[137],"journal":[138],"Groups,":[140],"Complexity,":[141],"Cryptology":[142]},"counts_by_year":[],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2025-10-10T00:00:00"}