{"id":"https://openalex.org/W2976734420","doi":"https://doi.org/10.1080/00029890.2020.1803625","title":"On a Theorem of Ledermann and Neumann","display_name":"On a Theorem of Ledermann and Neumann","publication_year":2020,"publication_date":"2020-10-20","ids":{"openalex":"https://openalex.org/W2976734420","doi":"https://doi.org/10.1080/00029890.2020.1803625","mag":"2976734420"},"language":"en","primary_location":{"id":"doi:10.1080/00029890.2020.1803625","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00029890.2020.1803625","pdf_url":null,"source":{"id":"https://openalex.org/S156280010","display_name":"American Mathematical Monthly","issn_l":"0002-9890","issn":["0002-9890","1930-0972"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The American Mathematical Monthly","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/1909.13220","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5066540439","display_name":"Benjamin Sambale","orcid":"https://orcid.org/0000-0001-9914-1652"},"institutions":[{"id":"https://openalex.org/I114112103","display_name":"Leibniz University Hannover","ror":"https://ror.org/0304hq317","country_code":"DE","type":"education","lineage":["https://openalex.org/I114112103"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Benjamin Sambale","raw_affiliation_strings":["Institut f\u00fcr Algebra, Zahlentheorie und Diskrete Mathematik, Leibniz Universit\u00e4t Hannover, Welfengarten 1, 30167 Hannover, Germany","University of Jena"],"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Algebra, Zahlentheorie und Diskrete Mathematik, Leibniz Universit\u00e4t Hannover, Welfengarten 1, 30167 Hannover, Germany","institution_ids":["https://openalex.org/I114112103"]},{"raw_affiliation_string":"University of Jena","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5066540439"],"corresponding_institution_ids":["https://openalex.org/I114112103"],"apc_list":null,"apc_paid":null,"fwci":0.5476,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.55049261,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"127","issue":"9","first_page":"827","last_page":"834"},"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/T11797","display_name":"graph theory and CDMA systems","score":0.9973000288009644,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10304","display_name":"Geometric and Algebraic Topology","score":0.9940999746322632,"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/von-neumann-architecture","display_name":"Von Neumann architecture","score":0.8751238584518433},{"id":"https://openalex.org/keywords/automorphism","display_name":"Automorphism","score":0.7512431144714355},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6420029997825623},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.533921480178833},{"id":"https://openalex.org/keywords/von-neumann-algebra","display_name":"Von Neumann algebra","score":0.4304264783859253},{"id":"https://openalex.org/keywords/finitely-generated-abelian-group","display_name":"Finitely-generated abelian group","score":0.42814794182777405},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3369893729686737}],"concepts":[{"id":"https://openalex.org/C80469333","wikidata":"https://www.wikidata.org/wiki/Q189088","display_name":"Von Neumann architecture","level":2,"score":0.8751238584518433},{"id":"https://openalex.org/C118712358","wikidata":"https://www.wikidata.org/wiki/Q782566","display_name":"Automorphism","level":2,"score":0.7512431144714355},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6420029997825623},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.533921480178833},{"id":"https://openalex.org/C153408630","wikidata":"https://www.wikidata.org/wiki/Q1970172","display_name":"Von Neumann algebra","level":3,"score":0.4304264783859253},{"id":"https://openalex.org/C162860070","wikidata":"https://www.wikidata.org/wiki/Q142140","display_name":"Finitely-generated abelian group","level":2,"score":0.42814794182777405},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3369893729686737}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1080/00029890.2020.1803625","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00029890.2020.1803625","pdf_url":null,"source":{"id":"https://openalex.org/S156280010","display_name":"American Mathematical Monthly","issn_l":"0002-9890","issn":["0002-9890","1930-0972"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The American Mathematical Monthly","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1909.13220","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1909.13220","pdf_url":"https://arxiv.org/pdf/1909.13220","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:2976734420","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1909.13220.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.1909.13220","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1909.13220","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:1909.13220","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1909.13220","pdf_url":"https://arxiv.org/pdf/1909.13220","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":[],"awards":[{"id":"https://openalex.org/G2317804258","display_name":null,"funder_award_id":"SA 2864/3-1","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G4185455507","display_name":null,"funder_award_id":"SA 2864/1-2","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2976734420.pdf","grobid_xml":"https://content.openalex.org/works/W2976734420.grobid-xml"},"referenced_works_count":25,"referenced_works":["https://openalex.org/W1964760940","https://openalex.org/W1971882410","https://openalex.org/W1971899959","https://openalex.org/W1975802330","https://openalex.org/W1979677169","https://openalex.org/W1987762225","https://openalex.org/W2014701683","https://openalex.org/W2024256799","https://openalex.org/W2043780218","https://openalex.org/W2058091879","https://openalex.org/W2062449704","https://openalex.org/W2066923888","https://openalex.org/W2068312480","https://openalex.org/W2127560278","https://openalex.org/W2136761630","https://openalex.org/W2155683450","https://openalex.org/W2167116005","https://openalex.org/W2334079601","https://openalex.org/W2494541182","https://openalex.org/W2910966645","https://openalex.org/W2962898350","https://openalex.org/W2963450532","https://openalex.org/W3107182388","https://openalex.org/W3146176610","https://openalex.org/W4205466935"],"related_works":["https://openalex.org/W626536320","https://openalex.org/W2398066697","https://openalex.org/W1518709316","https://openalex.org/W3162549569","https://openalex.org/W2078179501","https://openalex.org/W985857651","https://openalex.org/W2364905853","https://openalex.org/W4441599","https://openalex.org/W2076847546","https://openalex.org/W3160581193","https://openalex.org/W3186373063","https://openalex.org/W2267250845","https://openalex.org/W1635668281","https://openalex.org/W1025907065","https://openalex.org/W2810657755","https://openalex.org/W1982786777","https://openalex.org/W1990882402","https://openalex.org/W437653794","https://openalex.org/W1489269973","https://openalex.org/W2333749935"],"abstract_inverted_index":{"It":[0],"is":[1,51],"easy":[2],"to":[3],"see":[4],"that":[5,25],"the":[6,26,42,55,86],"number":[7,43],"of":[8,10,14,28,44,46,74,80,88],"automorphisms":[9,45],"a":[11,29,37,69],"finite":[12,30],"group":[13,31],"order":[15,27],"n":[16],"cannot":[17],"exceed":[18],"n!.":[19],"Ledermann":[20],"and":[21,53,71],"Neumann":[22],"proved":[23],"conversely":[24],"G":[32],"can":[33],"be":[34],"bounded":[35],"by":[36,59],"function":[38],"depending":[39],"only":[40],"on":[41,78],"G.":[47],"While":[48],"their":[49],"proof":[50,73],"long":[52],"complicated,":[54],"result":[56],"was":[57],"rediscovered":[58],"Nagrebecki\u012d":[60],"14":[61],"years":[62],"later.":[63],"In":[64],"this":[65],"article,":[66],"we":[67],"give":[68],"short":[70],"elementary":[72],"Ledermann\u2013Neumann\u2019s":[75],"theorem":[76],"based":[77],"some":[79],"Nagrebecki\u012d\u2019s":[81],"arguments.":[82],"We":[83],"also":[84],"discuss":[85],"history":[87],"related":[89],"conjectures.":[90]},"counts_by_year":[{"year":2020,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}
