{"id":"https://openalex.org/W7220956545","doi":"https://doi.org/10.48550/arxiv.2610.09368","title":"Abelian composition factors of finite rational groups","display_name":"Abelian composition factors of finite rational groups","publication_year":2026,"publication_date":"2026-10-07","ids":{"openalex":"https://openalex.org/W7220956545","doi":"https://doi.org/10.48550/arxiv.2610.09368"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.09368","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.09368","pdf_url":"https://arxiv.org/pdf/2610.09368","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.09368","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101730184","display_name":"Junying Guo","orcid":"https://orcid.org/0000-0002-8219-1431","observed_orcids":["https://orcid.org/0000-0002-8219-1431"]},"institutions":[{"id":"https://openalex.org/I53592917","display_name":"Jiangxi Normal University","ror":"https://ror.org/05nkgk822","country_code":"CN","type":"education","lineage":["https://openalex.org/I53592917"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Guo, Junying","raw_affiliation_strings":["School of Mathematics and Statistics , Jiangxi Normal University , Nanchang , 330022 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics , Jiangxi Normal University , Nanchang , 330022 , China","institution_ids":["https://openalex.org/I53592917"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5157888393","display_name":"Yanjun Liu","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I53592917","display_name":"Jiangxi Normal University","ror":"https://ror.org/05nkgk822","country_code":"CN","type":"education","lineage":["https://openalex.org/I53592917"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Liu, Yanjun","raw_affiliation_strings":["School of Mathematics and Statistics , Jiangxi Normal University , Nanchang , 330022 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics , Jiangxi Normal University , Nanchang , 330022 , China","institution_ids":["https://openalex.org/I53592917"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100643588","display_name":"Huan Xiong","orcid":"https://orcid.org/0000-0001-5401-7834","observed_orcids":["https://orcid.org/0000-0001-5401-7834","https://orcid.org/0000-0001-9906-4765"]},"institutions":[{"id":"https://openalex.org/I204983213","display_name":"Harbin Institute of Technology","ror":"https://ror.org/01yqg2h08","country_code":"CN","type":"education","lineage":["https://openalex.org/I204983213"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiong, Huan","raw_affiliation_strings":["Institute for Advanced Study in Mathematics , Harbin Institute of Technology , Heilongjiang 150001 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Advanced Study in Mathematics , Harbin Institute of Technology , Heilongjiang 150001 , China","institution_ids":["https://openalex.org/I204983213"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10849","display_name":"Finite Group Theory Research","score":0.9990000128746033,"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":0.9990000128746033,"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/T11680","display_name":"Advanced Algebra and Geometry","score":0.00039999998989515007,"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/T10304","display_name":"Geometric and Algebraic Topology","score":9.999999747378752e-05,"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/thompson-s-conjecture","display_name":"Thompson's conjecture","score":0.7680000066757202},{"id":"https://openalex.org/keywords/composition-factors","display_name":"composition factors","score":0.6349999904632568},{"id":"https://openalex.org/keywords/finite-simple-groups","display_name":"finite simple groups","score":0.6520000100135803}],"concepts":[{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.8008000254631042},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7455000281333923},{"id":"https://openalex.org/C40231798","wikidata":"https://www.wikidata.org/wiki/Q1333743","display_name":"Composition (language)","level":2,"score":0.6531999707221985},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.489300012588501},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4853000044822693},{"id":"https://openalex.org/C2777404646","wikidata":"https://www.wikidata.org/wiki/Q1057968","display_name":"Finite group","level":3,"score":0.4715999960899353},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4375999867916107},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.40869998931884766},{"id":"https://openalex.org/C156330621","wikidata":"https://www.wikidata.org/wiki/Q3393476","display_name":"Rational point","level":3,"score":0.39169999957084656},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.38359999656677246},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.3612000048160553},{"id":"https://openalex.org/C46875033","wikidata":"https://www.wikidata.org/wiki/Q1244890","display_name":"Rational number","level":2,"score":0.3352999985218048},{"id":"https://openalex.org/C186746360","wikidata":"https://www.wikidata.org/wiki/Q759832","display_name":"Solvable group","level":3,"score":0.31679999828338623},{"id":"https://openalex.org/C14669601","wikidata":"https://www.wikidata.org/wiki/Q2293759","display_name":"Torsion subgroup","level":4,"score":0.30660000443458557},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.30489999055862427},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.2867000102996826},{"id":"https://openalex.org/C2779483109","wikidata":"https://www.wikidata.org/wiki/Q4681347","display_name":"Additive group","level":3,"score":0.2833000123500824},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.2777999937534332},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.27129998803138733},{"id":"https://openalex.org/C200681373","wikidata":"https://www.wikidata.org/wiki/Q1260803","display_name":"Rank of an abelian group","level":4,"score":0.26579999923706055},{"id":"https://openalex.org/C168167062","wikidata":"https://www.wikidata.org/wiki/Q1117970","display_name":"Component (thermodynamics)","level":2,"score":0.2653000056743622},{"id":"https://openalex.org/C81008192","wikidata":"https://www.wikidata.org/wiki/Q1017231","display_name":"Elementary abelian group","level":3,"score":0.2630000114440918},{"id":"https://openalex.org/C75190567","wikidata":"https://www.wikidata.org/wiki/Q41237","display_name":"Rational function","level":2,"score":0.2597000002861023},{"id":"https://openalex.org/C165637685","wikidata":"https://www.wikidata.org/wiki/Q5008459","display_name":"CA-group","level":3,"score":0.25600001215934753}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.09368","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.09368","pdf_url":"https://arxiv.org/pdf/2610.09368","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2610.09368","doi":"https://doi.org/10.48550/arxiv.2610.09368","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.09368","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.09368","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.09368","pdf_url":"https://arxiv.org/pdf/2610.09368","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G1844031539","display_name":null,"funder_award_id":"20232BAB202012","funder_id":"https://openalex.org/F4320322665","funder_display_name":"Natural Science Foundation of Jiangxi Province"},{"id":"https://openalex.org/G4611506324","display_name":null,"funder_award_id":"11761034","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322665","display_name":"Natural Science Foundation of Jiangxi Province","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7220956545.pdf","grobid_xml":"https://content.openalex.org/works/W7220956545.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W7167917487"],"related_works":["https://openalex.org/W2030553852","https://openalex.org/W2062220628","https://openalex.org/W2930125927","https://openalex.org/W2557640001","https://openalex.org/W4379517166","https://openalex.org/W2769871181","https://openalex.org/W2951014900","https://openalex.org/W2389567944","https://openalex.org/W1997398369","https://openalex.org/W2039594013"],"abstract_inverted_index":{"Motivated":[0],"by":[1],"an":[2],"observation":[3],"concerning":[4],"the":[5,38,45,57,60],"$S_3$-conjecture,":[6],"we":[7,32],"prove":[8],"that":[9,40],"every":[10],"abelian":[11],"composition":[12,53,62],"factor":[13],"of":[14,47,59,64],"a":[15],"finite":[16,65],"rational":[17,66],"group":[18],"has":[19],"order":[20],"$2$,":[21],"$3$,":[22],"or":[23],"$5$.":[24],"Thompson":[25],"previously":[26],"restricted":[27],"these":[28],"orders":[29],"to":[30],"$\\{2,3,5,7,11\\}$;":[31],"exclude":[33],"$7$":[34],"and":[35,49],"$11$,":[36],"establishing":[37],"bound":[39],"he":[41],"proposed.":[42],"Together":[43],"with":[44],"work":[46],"Feit":[48],"Seitz":[50],"on":[51],"nonabelian":[52],"factors,":[54],"this":[55],"completes":[56],"determination":[58],"possible":[61],"factors":[63],"groups.":[67]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-09T00:00:00"}
