{"id":"https://openalex.org/W4323857577","doi":"https://doi.org/10.1142/s021819672350025x","title":"Finite groups satisfying the independence property","display_name":"Finite groups satisfying the independence property","publication_year":2023,"publication_date":"2023-03-10","ids":{"openalex":"https://openalex.org/W4323857577","doi":"https://doi.org/10.1142/s021819672350025x"},"language":"en","primary_location":{"id":"doi:10.1142/s021819672350025x","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s021819672350025x","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":true,"oa_status":"green","oa_url":"https://research-repository.st-andrews.ac.uk/bitstream/10023/27605/1/independence_and_perfect_rank.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5051756142","display_name":"Saul D. Freedman","orcid":"https://orcid.org/0000-0001-8062-0549"},"institutions":[{"id":"https://openalex.org/I16835326","display_name":"University of St Andrews","ror":"https://ror.org/02wn5qz54","country_code":"GB","type":"education","lineage":["https://openalex.org/I16835326"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Saul D. Freedman","raw_affiliation_strings":["School of Mathematics and Statistics, University of St Andrews, St Andrews, KY16 9SS, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, University of St Andrews, St Andrews, KY16 9SS, UK","institution_ids":["https://openalex.org/I16835326"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5076770399","display_name":"Andrea Lucchini","orcid":"https://orcid.org/0000-0002-2134-4991"},"institutions":[{"id":"https://openalex.org/I138689650","display_name":"University of Padua","ror":"https://ror.org/00240q980","country_code":"IT","type":"education","lineage":["https://openalex.org/I138689650"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Andrea Lucchini","raw_affiliation_strings":["Universit\u00e0 di Padova, Dipartimento di Matematica, \u201cTullio Levi-Civita\u201d Via Trieste 63, 35121 Padova, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00e0 di Padova, Dipartimento di Matematica, \u201cTullio Levi-Civita\u201d Via Trieste 63, 35121 Padova, Italy","institution_ids":["https://openalex.org/I138689650"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5067214307","display_name":"Daniele Nemmi","orcid":"https://orcid.org/0000-0003-4550-8636"},"institutions":[{"id":"https://openalex.org/I138689650","display_name":"University of Padua","ror":"https://ror.org/00240q980","country_code":"IT","type":"education","lineage":["https://openalex.org/I138689650"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Daniele Nemmi","raw_affiliation_strings":["Universit\u00e0 di Padova, Dipartimento di Matematica, \u201cTullio Levi-Civita\u201d Via Trieste 63, 35121 Padova, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00e0 di Padova, Dipartimento di Matematica, \u201cTullio Levi-Civita\u201d Via Trieste 63, 35121 Padova, Italy","institution_ids":["https://openalex.org/I138689650"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5030261802","display_name":"Colva M. Roney\u2010Dougal","orcid":"https://orcid.org/0000-0002-0532-3349"},"institutions":[{"id":"https://openalex.org/I16835326","display_name":"University of St Andrews","ror":"https://ror.org/02wn5qz54","country_code":"GB","type":"education","lineage":["https://openalex.org/I16835326"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Colva M. Roney-Dougal","raw_affiliation_strings":["School of Mathematics and Statistics, University of St Andrews, St Andrews, KY16 9SS, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, University of St Andrews, St Andrews, KY16 9SS, UK","institution_ids":["https://openalex.org/I16835326"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5076770399"],"corresponding_institution_ids":["https://openalex.org/I138689650"],"apc_list":null,"apc_paid":null,"fwci":2.6449,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.88503832,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"33","issue":"03","first_page":"509","last_page":"545"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10849","display_name":"Finite Group Theory Research","score":0.9998999834060669,"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":0.9998999834060669,"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/T11130","display_name":"Coding theory and cryptography","score":0.9959999918937683,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9958999752998352,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.9102441072463989},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.6014911532402039},{"id":"https://openalex.org/keywords/pairwise-comparison","display_name":"Pairwise comparison","score":0.5525444149971008},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.5523317456245422},{"id":"https://openalex.org/keywords/independence","display_name":"Independence (probability theory)","score":0.5260553359985352},{"id":"https://openalex.org/keywords/finite-group","display_name":"Finite group","score":0.5203539729118347},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5004632472991943},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4644968509674072},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.43496984243392944},{"id":"https://openalex.org/keywords/element","display_name":"Element (criminal law)","score":0.43141621351242065},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.42346665263175964},{"id":"https://openalex.org/keywords/law","display_name":"Law","score":0.06199634075164795}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9102441072463989},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.6014911532402039},{"id":"https://openalex.org/C184898388","wikidata":"https://www.wikidata.org/wiki/Q1435712","display_name":"Pairwise comparison","level":2,"score":0.5525444149971008},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.5523317456245422},{"id":"https://openalex.org/C35651441","wikidata":"https://www.wikidata.org/wiki/Q625303","display_name":"Independence (probability theory)","level":2,"score":0.5260553359985352},{"id":"https://openalex.org/C2777404646","wikidata":"https://www.wikidata.org/wiki/Q1057968","display_name":"Finite group","level":3,"score":0.5203539729118347},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5004632472991943},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4644968509674072},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.43496984243392944},{"id":"https://openalex.org/C200288055","wikidata":"https://www.wikidata.org/wiki/Q2621792","display_name":"Element (criminal law)","level":2,"score":0.43141621351242065},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.42346665263175964},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.06199634075164795},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"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/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1142/s021819672350025x","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s021819672350025x","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:research-repository.st-andrews.ac.uk:10023/27605","is_oa":true,"landing_page_url":"https://hdl.handle.net/10023/27605","pdf_url":"https://research-repository.st-andrews.ac.uk/bitstream/10023/27605/1/independence_and_perfect_rank.pdf","source":{"id":"https://openalex.org/S4306400230","display_name":"St Andrews Research Repository (St Andrews Research Repository)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I16835326","host_organization_name":"University of St Andrews","host_organization_lineage":["https://openalex.org/I16835326"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Journal article"},{"id":"pmh:oai:www.research.unipd.it:11577/3494785","is_oa":true,"landing_page_url":"https://hdl.handle.net/11577/3494785","pdf_url":"https://www.research.unipd.it/bitstream/11577/3494785/2/2208.04064v2.pdf","source":{"id":"https://openalex.org/S4377196283","display_name":"Research Padua  Archive (University of Padua)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I138689650","host_organization_name":"University of Padua","host_organization_lineage":["https://openalex.org/I138689650"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:research-repository.st-andrews.ac.uk:10023/27605","is_oa":true,"landing_page_url":"https://hdl.handle.net/10023/27605","pdf_url":"https://research-repository.st-andrews.ac.uk/bitstream/10023/27605/1/independence_and_perfect_rank.pdf","source":{"id":"https://openalex.org/S4306400230","display_name":"St Andrews Research Repository (St Andrews Research Repository)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I16835326","host_organization_name":"University of St Andrews","host_organization_lineage":["https://openalex.org/I16835326"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Journal article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2203179303","display_name":null,"funder_award_id":"R014604/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G3341554066","display_name":null,"funder_award_id":"EP/R014604/","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G3691759950","display_name":null,"funder_award_id":"EP/R014604/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G5450091064","display_name":"Isaac Newton Institute for Mathematical Sciences","funder_award_id":"EP/R014604/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G6226214964","display_name":null,"funder_award_id":"EP/R014604","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320320278","display_name":"University of St Andrews","ror":"https://ror.org/02wn5qz54"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"},{"id":"https://openalex.org/F4320337380","display_name":"Division of Mathematical Sciences","ror":"https://ror.org/051fftw81"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4323857577.pdf"},"referenced_works_count":50,"referenced_works":["https://openalex.org/W61179199","https://openalex.org/W656473322","https://openalex.org/W1493654001","https://openalex.org/W1965762980","https://openalex.org/W1976677460","https://openalex.org/W1993935239","https://openalex.org/W2005033974","https://openalex.org/W2005832340","https://openalex.org/W2006879104","https://openalex.org/W2014387404","https://openalex.org/W2019780075","https://openalex.org/W2022456803","https://openalex.org/W2024969197","https://openalex.org/W2031685413","https://openalex.org/W2033300661","https://openalex.org/W2043225560","https://openalex.org/W2055566058","https://openalex.org/W2062417018","https://openalex.org/W2064441649","https://openalex.org/W2082411272","https://openalex.org/W2095639635","https://openalex.org/W2115609066","https://openalex.org/W2118638316","https://openalex.org/W2120565842","https://openalex.org/W2123656616","https://openalex.org/W2129355152","https://openalex.org/W2146337808","https://openalex.org/W2297033384","https://openalex.org/W2583234340","https://openalex.org/W2610449376","https://openalex.org/W2917893419","https://openalex.org/W2920263613","https://openalex.org/W2963357159","https://openalex.org/W2964023986","https://openalex.org/W2964119372","https://openalex.org/W3014882618","https://openalex.org/W3042124501","https://openalex.org/W3044270079","https://openalex.org/W3102747723","https://openalex.org/W3108859253","https://openalex.org/W3110704126","https://openalex.org/W3126524697","https://openalex.org/W3200289635","https://openalex.org/W3208305474","https://openalex.org/W4206967995","https://openalex.org/W4213060864","https://openalex.org/W4213264348","https://openalex.org/W4214600076","https://openalex.org/W4245553968","https://openalex.org/W4293176479"],"related_works":["https://openalex.org/W2487162673","https://openalex.org/W2949152769","https://openalex.org/W4372354731","https://openalex.org/W2562400057","https://openalex.org/W1692008701","https://openalex.org/W2597588799","https://openalex.org/W4360593462","https://openalex.org/W2194570607","https://openalex.org/W2807634898","https://openalex.org/W2185177341"],"abstract_inverted_index":{"We":[0,48],"say":[1],"that":[2,64,80,94],"a":[3,30,43,50,77],"finite":[4,55,84],"group":[5,67],"G":[6,35],"satisfies":[7],"the":[8,46,54,95,105],"independence":[9],"property":[10],"if,":[11],"for":[12,34],"every":[13,65],"pair":[14],"of":[15,21,38,45,53,73,98,107],"distinct":[16],"elements":[17],"x":[18,39],"and":[19,40,60],"y":[20,41],"G,":[22],"either":[23],"[Formula:":[24],"see":[25],"text]":[26],"is":[27,42,68,76],"contained":[28],"in":[29,61],"minimal":[31],"generating":[32],"set":[33],"or":[36],"one":[37],"power":[44],"other.":[47],"give":[49],"complete":[51],"classification":[52],"groups":[56,87],"with":[57],"this":[58],"property,":[59],"particular":[62],"prove":[63],"such":[66,93],"supersoluble.":[69],"A":[70],"key":[71],"ingredient":[72],"our":[74],"proof":[75],"theorem":[78],"showing":[79],"all":[81],"but":[82,102],"three":[83],"almost":[85],"simple":[86],"H":[88,99],"contain":[89],"an":[90],"element":[91],"s":[92],"maximal":[96],"subgroups":[97],"containing":[100,104],"s,":[101],"not":[103],"socle":[106],"H,":[108],"are":[109],"pairwise":[110],"non-conjugate.":[111]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1}],"updated_date":"2026-05-19T08:33:51.333923","created_date":"2025-10-10T00:00:00"}