{"id":"https://openalex.org/W2346830252","doi":"https://doi.org/10.1142/s0218196717500503","title":"Configuration equivalence is not equivalent to isomorphism","display_name":"Configuration equivalence is not equivalent to isomorphism","publication_year":2017,"publication_date":"2017-11-08","ids":{"openalex":"https://openalex.org/W2346830252","doi":"https://doi.org/10.1142/s0218196717500503","mag":"2346830252"},"language":"en","primary_location":{"id":"doi:10.1142/s0218196717500503","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196717500503","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":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1605.00781","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5004243959","display_name":"Ali Rejali","orcid":"https://orcid.org/0000-0001-7270-665X"},"institutions":[{"id":"https://openalex.org/I39268498","display_name":"University of Isfahan","ror":"https://ror.org/05h9t7759","country_code":"IR","type":"education","lineage":["https://openalex.org/I39268498"]}],"countries":["IR"],"is_corresponding":true,"raw_author_name":"Ali Rejali","raw_affiliation_strings":["Department of Mathematics, University of Isfahan, Isfahan, 81746-73441, Iran","Department of Mathematics, University of Isfahan, Isfahan 81746\u201373441, Iran"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Isfahan, Isfahan, 81746-73441, Iran","institution_ids":["https://openalex.org/I39268498"]},{"raw_affiliation_string":"Department of Mathematics, University of Isfahan, Isfahan 81746\u201373441, Iran","institution_ids":["https://openalex.org/I39268498"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5044008769","display_name":"Meisam Soleimani Malekan","orcid":"https://orcid.org/0000-0002-4521-1325"},"institutions":[{"id":"https://openalex.org/I39268498","display_name":"University of Isfahan","ror":"https://ror.org/05h9t7759","country_code":"IR","type":"education","lineage":["https://openalex.org/I39268498"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Meisam Soleimani Malekan","raw_affiliation_strings":["Department of Mathematics, University of Isfahan, Isfahan, 81746-73441, Iran","Department of Mathematics, University of Isfahan, Isfahan 81746\u201373441, Iran"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Isfahan, Isfahan, 81746-73441, Iran","institution_ids":["https://openalex.org/I39268498"]},{"raw_affiliation_string":"Department of Mathematics, University of Isfahan, Isfahan 81746\u201373441, Iran","institution_ids":["https://openalex.org/I39268498"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5004243959"],"corresponding_institution_ids":["https://openalex.org/I39268498"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.04633205,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"27","issue":"08","first_page":"1073","last_page":"1085"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10849","display_name":"Finite Group Theory Research","score":0.9952999949455261,"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"}},"topics":[{"id":"https://openalex.org/T10849","display_name":"Finite Group Theory Research","score":0.9952999949455261,"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"}},{"id":"https://openalex.org/T11703","display_name":"Rings, Modules, and Algebras","score":0.9937999844551086,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/T11673","display_name":"Advanced Topics in Algebra","score":0.9710000157356262,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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":0.7621328830718994},{"id":"https://openalex.org/keywords/isomorphism","display_name":"Isomorphism (crystallography)","score":0.7210363149642944},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.6275190711021423},{"id":"https://openalex.org/keywords/abelian-group","display_name":"Abelian group","score":0.6095266342163086},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.6054762601852417},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4711552858352661},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.46292826533317566},{"id":"https://openalex.org/keywords/group-isomorphism","display_name":"Group isomorphism","score":0.4335886538028717},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.43195903301239014},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.39754024147987366},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3670090436935425},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3405068516731262},{"id":"https://openalex.org/keywords/automorphism","display_name":"Automorphism","score":0.10863777995109558},{"id":"https://openalex.org/keywords/automorphism-group","display_name":"Automorphism group","score":0.08336323499679565}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7621328830718994},{"id":"https://openalex.org/C203436722","wikidata":"https://www.wikidata.org/wiki/Q902950","display_name":"Isomorphism (crystallography)","level":3,"score":0.7210363149642944},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.6275190711021423},{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.6095266342163086},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.6054762601852417},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4711552858352661},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.46292826533317566},{"id":"https://openalex.org/C155190451","wikidata":"https://www.wikidata.org/wiki/Q742064","display_name":"Group isomorphism","level":5,"score":0.4335886538028717},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.43195903301239014},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.39754024147987366},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3670090436935425},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3405068516731262},{"id":"https://openalex.org/C118712358","wikidata":"https://www.wikidata.org/wiki/Q782566","display_name":"Automorphism","level":2,"score":0.10863777995109558},{"id":"https://openalex.org/C2988750069","wikidata":"https://www.wikidata.org/wiki/Q60790315","display_name":"Automorphism group","level":3,"score":0.08336323499679565},{"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/C8010536","wikidata":"https://www.wikidata.org/wiki/Q160398","display_name":"Crystallography","level":1,"score":0.0},{"id":"https://openalex.org/C124453015","wikidata":"https://www.wikidata.org/wiki/Q1139583","display_name":"Inner automorphism","level":4,"score":0.0},{"id":"https://openalex.org/C115624301","wikidata":"https://www.wikidata.org/wiki/Q895901","display_name":"Crystal structure","level":2,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1142/s0218196717500503","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196717500503","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":"pmh:oai:arXiv.org:1605.00781","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1605.00781","pdf_url":"https://arxiv.org/pdf/1605.00781","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:2346830252","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1605.00781.pdf","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":"doi:10.48550/arxiv.1605.00781","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1605.00781","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":"pmh:oai:arXiv.org:1605.00781","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1605.00781","pdf_url":"https://arxiv.org/pdf/1605.00781","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"},"sustainable_development_goals":[{"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.4699999988079071}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2346830252.pdf","grobid_xml":"https://content.openalex.org/works/W2346830252.grobid-xml"},"referenced_works_count":5,"referenced_works":["https://openalex.org/W648760579","https://openalex.org/W1493863997","https://openalex.org/W1506327821","https://openalex.org/W2042908323","https://openalex.org/W2962898801"],"related_works":["https://openalex.org/W2963330391","https://openalex.org/W2750702241","https://openalex.org/W2737755177","https://openalex.org/W2789530262","https://openalex.org/W2322831583","https://openalex.org/W2980518627","https://openalex.org/W2951572560","https://openalex.org/W2313029091","https://openalex.org/W2333723162","https://openalex.org/W2805181198","https://openalex.org/W3151400279","https://openalex.org/W103515877","https://openalex.org/W2790391813","https://openalex.org/W3168489229","https://openalex.org/W2072138112","https://openalex.org/W3018088990","https://openalex.org/W2319562546","https://openalex.org/W16856791","https://openalex.org/W2108954063","https://openalex.org/W2937467752"],"abstract_inverted_index":{"Giving":[0],"a":[1],"condition":[2],"for":[3],"the":[4,13,18,21,23,26,33,70,75,80],"amenability":[5],"of":[6,15,20,28,35,79],"groups,":[7],"Rosenblatt":[8,66],"and":[9,50,67],"Willis":[10],"first":[11],"introduced":[12],"concept":[14,27,34],"configuration.":[16],"From":[17],"beginning":[19],"theory,":[22],"question":[24,44],"whether":[25,69],"configuration":[29,56,71],"equivalence":[30],"coincides":[31],"with":[32],"group":[36,78],"isomorphism":[37],"was":[38],"posed.":[39],"We":[40,85],"negatively":[41],"answer":[42],"this":[43,62],"by":[45],"introducing":[46],"two":[47],"non-isomorphic,":[48],"solvable":[49],"hence":[51],"amenable":[52],"groups":[53,73,90],"which":[54],"are":[55],"equivalent.":[57],"Also,":[58],"we":[59],"will":[60],"prove":[61],"conjecture,":[63],"due":[64],"to":[65],"Willis,":[68],"equivalent":[72,89],"include":[74],"free":[76],"non-Abelian":[77],"same":[81,92],"rank":[82],"or":[83],"not.":[84],"show":[86],"that":[87],"two-sided":[88],"have":[91],"class":[93],"numbers.":[94]},"counts_by_year":[],"updated_date":"2026-02-09T09:26:11.010843","created_date":"2025-10-10T00:00:00"}