{"id":"https://openalex.org/W4406583945","doi":"https://doi.org/10.1142/s0218196725500067","title":"Two results on complexities of decision problems of groups","display_name":"Two results on complexities of decision problems of groups","publication_year":2025,"publication_date":"2025-01-18","ids":{"openalex":"https://openalex.org/W4406583945","doi":"https://doi.org/10.1142/s0218196725500067"},"language":"en","primary_location":{"id":"doi:10.1142/s0218196725500067","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196725500067","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"],"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/A5022967955","display_name":"Uri Andrews","orcid":"https://orcid.org/0000-0002-4653-7458"},"institutions":[{"id":"https://openalex.org/I135310074","display_name":"University of Wisconsin\u2013Madison","ror":"https://ror.org/01y2jtd41","country_code":"US","type":"education","lineage":["https://openalex.org/I135310074"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Uri Andrews","raw_affiliation_strings":["Department of Mathematics, University of Wisconsin - Madison, 480 Lincoln Drive Madison, WI 53706 United States of America"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Wisconsin - Madison, 480 Lincoln Drive Madison, WI 53706 United States of America","institution_ids":["https://openalex.org/I135310074"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5027707580","display_name":"Matthew Harrison\u2010Trainor","orcid":null},"institutions":[{"id":"https://openalex.org/I39422238","display_name":"University of Illinois Chicago","ror":"https://ror.org/02mpq6x41","country_code":"US","type":"education","lineage":["https://openalex.org/I39422238"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Matthew Harrison-Trainor","raw_affiliation_strings":["Department of Mathematics, Statistics, and Computer Science University of Illinois Chicago, 851 S.\u00a0Morgan Street Chicago, IL 60607 United States of America"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Statistics, and Computer Science University of Illinois Chicago, 851 S.\u00a0Morgan Street Chicago, IL 60607 United States of America","institution_ids":["https://openalex.org/I39422238"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5063666725","display_name":"Turbo Ho","orcid":null},"institutions":[{"id":"https://openalex.org/I157638225","display_name":"California State University, Northridge","ror":"https://ror.org/005f5hv41","country_code":"US","type":"education","lineage":["https://openalex.org/I157638225"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Meng-Che \u201cTurbo\u201d Ho","raw_affiliation_strings":["Department of Mathematics California State University, Northridge 18111 Nordhoff Street Northridge, CA 91330, United States of America"],"raw_orcid":"https://orcid.org/0000-0001-6292-6835","affiliations":[{"raw_affiliation_string":"Department of Mathematics California State University, Northridge 18111 Nordhoff Street Northridge, CA 91330, United States of America","institution_ids":["https://openalex.org/I157638225"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5022967955"],"corresponding_institution_ids":["https://openalex.org/I135310074"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.02805329,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"35","issue":"02","first_page":"311","last_page":"327"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.5049999952316284,"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/T11476","display_name":"Graph theory and applications","score":0.5049999952316284,"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/mathematics","display_name":"Mathematics","score":0.8964439630508423},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3820171654224396},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.3462297320365906},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.3264538645744324},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.29440927505493164},{"id":"https://openalex.org/keywords/medicine","display_name":"Medicine","score":0.07153552770614624}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8964439630508423},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3820171654224396},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3462297320365906},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.3264538645744324},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.29440927505493164},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.07153552770614624},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218196725500067","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196725500067","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W1909320839","https://openalex.org/W1967684312","https://openalex.org/W2001162243","https://openalex.org/W2043152523","https://openalex.org/W2053852843","https://openalex.org/W2058701006","https://openalex.org/W2079926883","https://openalex.org/W2319243709","https://openalex.org/W2333555861","https://openalex.org/W2535111425","https://openalex.org/W2558071339","https://openalex.org/W2558322769","https://openalex.org/W2772134068","https://openalex.org/W2963065069","https://openalex.org/W3039201404","https://openalex.org/W4293176479","https://openalex.org/W4376565638"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2962838298","https://openalex.org/W2600246793"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"answer":[4,78],"two":[5],"questions":[6],"on":[7],"the":[8,24,27,38,41,49,57,60,75,79,93,102,116],"complexities":[9],"of":[10,13,26,59,63,84,87,95,105],"decision":[11],"problems":[12],"groups,":[14],"each":[15],"related":[16],"to":[17,101],"a":[18,64,106],"classical":[19],"result.":[20],"First,":[21],"Miller":[22],"characterized":[23],"complexity":[25],"isomorphism":[28,42],"problem":[29,43,62,104],"for":[30,40,44,82],"finitely":[31,65,107],"presented":[32,46,66,108],"groups":[33],"in":[34,74],"1971.":[35],"We":[36,77,90],"do":[37],"same":[39],"recursively":[45],"groups.":[47],"Second,":[48],"fact":[50],"that":[51,92],"every":[52],"Turing":[53,88],"degree":[54,58],"appears":[55],"as":[56],"word":[61,103],"group":[67,109],"is":[68,110,115],"shown":[69],"independently":[70],"by":[71],"multiple":[72],"people":[73],"1960s.":[76],"analogous":[80],"question":[81],"degrees":[83],"ceers":[85,96],"instead":[86],"degrees.":[89],"show":[91],"set":[94],"which":[97,114],"are":[98],"computably":[99],"equivalent":[100],"[Formula:":[111],"see":[112],"text]-complete,":[113],"maximal":[117],"possible":[118],"complexity.":[119]},"counts_by_year":[],"updated_date":"2026-05-21T09:19:25.381259","created_date":"2025-10-10T00:00:00"}