{"id":"https://openalex.org/W4415003705","doi":"https://doi.org/10.1109/lics65433.2025.00026","title":"The Identity Problem in virtually solvable matrix groups over algebraic numbers","display_name":"The Identity Problem in virtually solvable matrix groups over algebraic numbers","publication_year":2025,"publication_date":"2025-06-23","ids":{"openalex":"https://openalex.org/W4415003705","doi":"https://doi.org/10.1109/lics65433.2025.00026"},"language":"en","primary_location":{"id":"doi:10.1109/lics65433.2025.00026","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lics65433.2025.00026","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2025 40th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5063745100","display_name":"Corentin Bodart","orcid":null},"institutions":[{"id":"https://openalex.org/I4210120676","display_name":"Mathematical Institute of the Slovak Academy of Sciences","ror":"https://ror.org/02fhy7464","country_code":"SK","type":"facility","lineage":["https://openalex.org/I207624831","https://openalex.org/I4210120676"]}],"countries":["SK"],"is_corresponding":true,"raw_author_name":"Corentin Bodart","raw_affiliation_strings":["University of Oxford,Mathematical Institute,Oxford,United Kingdom"],"affiliations":[{"raw_affiliation_string":"University of Oxford,Mathematical Institute,Oxford,United Kingdom","institution_ids":["https://openalex.org/I4210120676"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5014183475","display_name":"Ruiwen Dong","orcid":"https://orcid.org/0009-0007-4349-082X"},"institutions":[{"id":"https://openalex.org/I2800082484","display_name":"Northeast Catholic College","ror":"https://ror.org/00rwtwt20","country_code":"US","type":"education","lineage":["https://openalex.org/I2800082484"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ruiwen Dong","raw_affiliation_strings":["University of Oxford,Magdalen College,Oxford,United Kingdom"],"affiliations":[{"raw_affiliation_string":"University of Oxford,Magdalen College,Oxford,United Kingdom","institution_ids":["https://openalex.org/I2800082484"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5063745100"],"corresponding_institution_ids":["https://openalex.org/I4210120676"],"apc_list":null,"apc_paid":null,"fwci":4.1252,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.94128909,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":null,"issue":null,"first_page":"249","last_page":"261"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13234","display_name":"advanced mathematical theories","score":0.8944000005722046,"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"}},"topics":[{"id":"https://openalex.org/T13234","display_name":"advanced mathematical theories","score":0.8944000005722046,"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/undecidable-problem","display_name":"Undecidable problem","score":0.824999988079071},{"id":"https://openalex.org/keywords/decidability","display_name":"Decidability","score":0.8080999851226807},{"id":"https://openalex.org/keywords/identity-matrix","display_name":"Identity matrix","score":0.5048999786376953},{"id":"https://openalex.org/keywords/identity","display_name":"Identity (music)","score":0.49970000982284546},{"id":"https://openalex.org/keywords/nilpotent-group","display_name":"Nilpotent group","score":0.4932999908924103},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.4629000127315521},{"id":"https://openalex.org/keywords/solvable-group","display_name":"Solvable group","score":0.45719999074935913},{"id":"https://openalex.org/keywords/nilpotent","display_name":"Nilpotent","score":0.4562999904155731}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.853600025177002},{"id":"https://openalex.org/C192034797","wikidata":"https://www.wikidata.org/wiki/Q3502995","display_name":"Undecidable problem","level":3,"score":0.824999988079071},{"id":"https://openalex.org/C153269930","wikidata":"https://www.wikidata.org/wiki/Q430001","display_name":"Decidability","level":2,"score":0.8080999851226807},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5583000183105469},{"id":"https://openalex.org/C134567657","wikidata":"https://www.wikidata.org/wiki/Q193794","display_name":"Identity matrix","level":3,"score":0.5048999786376953},{"id":"https://openalex.org/C2778355321","wikidata":"https://www.wikidata.org/wiki/Q17079427","display_name":"Identity (music)","level":2,"score":0.49970000982284546},{"id":"https://openalex.org/C206219070","wikidata":"https://www.wikidata.org/wiki/Q1755242","display_name":"Nilpotent group","level":3,"score":0.4932999908924103},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.48249998688697815},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.4629000127315521},{"id":"https://openalex.org/C186746360","wikidata":"https://www.wikidata.org/wiki/Q759832","display_name":"Solvable group","level":3,"score":0.45719999074935913},{"id":"https://openalex.org/C50555996","wikidata":"https://www.wikidata.org/wiki/Q840023","display_name":"Nilpotent","level":2,"score":0.4562999904155731},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.45410001277923584},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4277999997138977},{"id":"https://openalex.org/C24276413","wikidata":"https://www.wikidata.org/wiki/Q1050120","display_name":"Matrix group","level":3,"score":0.4023999869823456},{"id":"https://openalex.org/C58249144","wikidata":"https://www.wikidata.org/wiki/Q7597316","display_name":"Stallings theorem about ends of groups","level":3,"score":0.3594000041484833},{"id":"https://openalex.org/C162860070","wikidata":"https://www.wikidata.org/wiki/Q142140","display_name":"Finitely-generated abelian group","level":2,"score":0.3544999957084656},{"id":"https://openalex.org/C2780811992","wikidata":"https://www.wikidata.org/wiki/Q21083858","display_name":"Finitely generated group","level":3,"score":0.34130001068115234},{"id":"https://openalex.org/C115988155","wikidata":"https://www.wikidata.org/wiki/Q3262192","display_name":"Decision problem","level":2,"score":0.3314000070095062},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.30559998750686646},{"id":"https://openalex.org/C90988201","wikidata":"https://www.wikidata.org/wiki/Q255912","display_name":"Word problem (mathematics education)","level":2,"score":0.29350000619888306},{"id":"https://openalex.org/C81651864","wikidata":"https://www.wikidata.org/wiki/Q874429","display_name":"Group theory","level":2,"score":0.2912999987602234},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2786000072956085},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.2703999876976013}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/lics65433.2025.00026","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lics65433.2025.00026","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2025 40th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W562218106","https://openalex.org/W586599434","https://openalex.org/W1496801598","https://openalex.org/W1908282360","https://openalex.org/W1985927005","https://openalex.org/W1989605444","https://openalex.org/W2000011692","https://openalex.org/W2037418280","https://openalex.org/W2040034546","https://openalex.org/W2050829703","https://openalex.org/W2072901418","https://openalex.org/W2096390054","https://openalex.org/W2113555467","https://openalex.org/W2183852072","https://openalex.org/W2261634751","https://openalex.org/W2329237579","https://openalex.org/W2963164018","https://openalex.org/W4238472920","https://openalex.org/W4251324924","https://openalex.org/W4389314430","https://openalex.org/W4399523488","https://openalex.org/W4400179237"],"related_works":[],"abstract_inverted_index":{"The":[0],"Tits":[1],"alternative":[2],"states":[3],"that":[4,60],"a":[5,12,37,51,56],"finitely":[6,39,53],"generated":[7,40,54],"matrix":[8,31,68,120],"group":[9],"either":[10],"contains":[11],"nonabelian":[13],"free":[14],"subgroup":[15],"F2,":[16,125],"or":[17],"it":[18],"is":[19],"virtually":[20,29,66],"solvable.":[21],"This":[22],"paper":[23],"considers":[24],"two":[25],"decision":[26,135],"problems":[27,62],"in":[28,65,119],"solvable":[30,67],"groups:":[32],"the":[33,43,47,71,84,97,107,111,130],"Identity":[34,108],"Problem":[35,49,109,113],"(does":[36],"given":[38,52],"subsemigroup":[41,55],"contain":[42],"identity":[44],"matrix?),":[45],"and":[46,94,96,110],"Group":[48,112],"(is":[50],"group?).":[57],"We":[58],"show":[59],"both":[61,134],"are":[63,114],"decidable":[64],"groups":[69,89,102,121],"over":[70],"field":[72],"of":[73],"algebraic":[74],"numbers":[75],"$\\overline":[76],"{\\mathbb{Q}}":[77],"$":[78],".":[79],"Our":[80],"proof":[81],"also":[82],"extends":[83],"decidability":[85,98,131],"result":[86,99,127],"for":[87,100,133],"nilpotent":[88],"by":[90,103],"Bodart,":[91],"Ciobanu,":[92],"Metcalfe":[93],"Shaffrir,":[95],"metabelian":[101],"Dong":[104],"(STOC\u201924).":[105],"Since":[106],"known":[115],"to":[116],"be":[117],"undecidable":[118],"containing":[122],"F2":[123],"\u00d7":[124],"our":[126],"significantly":[128],"reduces":[129],"gap":[132],"problems.":[136]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-03-07T16:01:11.037858","created_date":"2025-10-10T00:00:00"}
