{"id":"https://openalex.org/W7223875876","doi":"https://doi.org/10.48550/arxiv.2610.34680","title":"Abelian quotients and orbit sizes for subgroups of linear groups","display_name":"Abelian quotients and orbit sizes for subgroups of linear groups","publication_year":2026,"publication_date":"2026-10-26","ids":{"openalex":"https://openalex.org/W7223875876","doi":"https://doi.org/10.48550/arxiv.2610.34680"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.34680","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.34680","pdf_url":"https://arxiv.org/pdf/2610.34680","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","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.34680","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5159769178","display_name":"Yong Yang","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Yang, Yong","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5159769178"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"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":0.9994999766349792,"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":0.9994999766349792,"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":9.999999747378752e-05,"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/T11703","display_name":"Rings, Modules, and Algebras","score":0.0,"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/abelian-quotients","display_name":"abelian quotients","score":0.9290000200271606},{"id":"https://openalex.org/keywords/orbit-size","display_name":"orbit size","score":0.8149999976158142},{"id":"https://openalex.org/keywords/finite-linear-groups","display_name":"finite linear groups","score":0.9480000138282776},{"id":"https://openalex.org/keywords/regular-orbits","display_name":"regular orbits","score":0.6150000095367432},{"id":"https://openalex.org/keywords/nilpotent-subgroups","display_name":"nilpotent subgroups","score":0.9909999966621399},{"id":"https://openalex.org/keywords/completely-reducible-modules","display_name":"completely reducible modules","score":0.9779999852180481},{"id":"https://openalex.org/keywords/mixed-characteristic","display_name":"mixed characteristic","score":0.9829999804496765},{"id":"https://openalex.org/keywords/fitting-subgroup","display_name":"Fitting subgroup","score":0.5440000295639038}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8452000021934509},{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.7840999960899353},{"id":"https://openalex.org/C199422724","wikidata":"https://www.wikidata.org/wiki/Q41118","display_name":"Quotient","level":2,"score":0.7616999745368958},{"id":"https://openalex.org/C196644772","wikidata":"https://www.wikidata.org/wiki/Q3884964","display_name":"Orbit (dynamics)","level":2,"score":0.6935999989509583},{"id":"https://openalex.org/C162838799","wikidata":"https://www.wikidata.org/wiki/Q596077","display_name":"Counterexample","level":2,"score":0.6079999804496765},{"id":"https://openalex.org/C50555996","wikidata":"https://www.wikidata.org/wiki/Q840023","display_name":"Nilpotent","level":2,"score":0.5514000058174133},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4765999913215637},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.46709999442100525},{"id":"https://openalex.org/C186746360","wikidata":"https://www.wikidata.org/wiki/Q759832","display_name":"Solvable group","level":3,"score":0.4043000042438507},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.37599998712539673},{"id":"https://openalex.org/C206219070","wikidata":"https://www.wikidata.org/wiki/Q1755242","display_name":"Nilpotent group","level":3,"score":0.34529998898506165},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3409000039100647},{"id":"https://openalex.org/C81008192","wikidata":"https://www.wikidata.org/wiki/Q1017231","display_name":"Elementary abelian group","level":3,"score":0.3370000123977661},{"id":"https://openalex.org/C2777404646","wikidata":"https://www.wikidata.org/wiki/Q1057968","display_name":"Finite group","level":3,"score":0.3197000026702881},{"id":"https://openalex.org/C2779483109","wikidata":"https://www.wikidata.org/wiki/Q4681347","display_name":"Additive group","level":3,"score":0.30869999527931213},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.3059999942779541},{"id":"https://openalex.org/C14669601","wikidata":"https://www.wikidata.org/wiki/Q2293759","display_name":"Torsion subgroup","level":4,"score":0.2865999937057495},{"id":"https://openalex.org/C95627345","wikidata":"https://www.wikidata.org/wiki/Q1138961","display_name":"Quotient group","level":4,"score":0.2842000126838684},{"id":"https://openalex.org/C81651864","wikidata":"https://www.wikidata.org/wiki/Q874429","display_name":"Group theory","level":2,"score":0.28200000524520874},{"id":"https://openalex.org/C197623797","wikidata":"https://www.wikidata.org/wiki/Q1454111","display_name":"Free abelian group","level":5,"score":0.2750999927520752},{"id":"https://openalex.org/C134064494","wikidata":"https://www.wikidata.org/wiki/Q6664682","display_name":"Locally finite group","level":3,"score":0.2669999897480011},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.26100000739097595},{"id":"https://openalex.org/C160826032","wikidata":"https://www.wikidata.org/wiki/Q286972","display_name":"p-group","level":3,"score":0.2551000118255615}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.34680","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.34680","pdf_url":"https://arxiv.org/pdf/2610.34680","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.2610.34680","doi":"https://doi.org/10.48550/arxiv.2610.34680","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.34680","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":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.34680","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.34680","pdf_url":"https://arxiv.org/pdf/2610.34680","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":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7223875876.pdf","grobid_xml":"https://content.openalex.org/works/W7223875876.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4283156527","https://openalex.org/W7221011226","https://openalex.org/W1533894016","https://openalex.org/W2950035099","https://openalex.org/W2288607629","https://openalex.org/W1991990247","https://openalex.org/W4361285558","https://openalex.org/W4396918980","https://openalex.org/W2971456275","https://openalex.org/W7099294017"],"abstract_inverted_index":{"Keller":[0],"and":[1],"Yang":[2],"formulated":[3],"two":[4,27],"conjectures":[5,36],"relating":[6],"abelian":[7],"quotients":[8],"of":[9,11,57],"subgroups":[10,52],"finite":[12,39],"linear":[13],"groups":[14],"to":[15,23,53],"largest":[16],"orbit":[17],"sizes.":[18],"After":[19],"counterexamples":[20],"were":[21,30],"found":[22],"the":[24,61],"original":[25],"conjectures,":[26],"revised":[28,35],"versions":[29],"proposed.":[31],"We":[32,44],"prove":[33],"both":[34],"for":[37,50],"every":[38],"group":[40],"$G$":[41],"satisfying":[42],"$F(G)=F^*(G)$.":[43],"also":[45],"extend":[46],"a":[47],"regular-orbit":[48],"theorem":[49],"nilpotent":[51],"completely":[54],"reducible":[55],"modules":[56],"mixed":[58],"characteristic":[59],"under":[60],"same":[62],"hypothesis.":[63]},"counts_by_year":[],"updated_date":"2026-11-06T12:05:46.655746","created_date":"2026-10-28T00:00:00"}
