{"id":"https://openalex.org/W7203708703","doi":"https://doi.org/10.48550/arxiv.2608.14972","title":"Exponents of factorized groups and Kashina's conjecture for group-theoretical Hopf algebras","display_name":"Exponents of factorized groups and Kashina's conjecture for group-theoretical Hopf algebras","publication_year":2026,"publication_date":"2026-08-15","ids":{"openalex":"https://openalex.org/W7203708703","doi":"https://doi.org/10.48550/arxiv.2608.14972"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.14972","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.14972","pdf_url":"https://arxiv.org/pdf/2608.14972","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/2608.14972","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5109667124","display_name":"Ningyi Li","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I121797337","display_name":"Leiden University","ror":"https://ror.org/027bh9e22","country_code":"NL","type":"education","lineage":["https://openalex.org/I121797337"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Li, Ningyi","raw_affiliation_strings":["Leiden University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Leiden University","institution_ids":["https://openalex.org/I121797337"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5109667124","display_name":"Ningyi Li","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I121797337","display_name":"Leiden University","ror":"https://ror.org/027bh9e22","country_code":"NL","type":"education","lineage":["https://openalex.org/I121797337"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Li, Ningyi","raw_affiliation_strings":["Leiden University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Leiden University","institution_ids":["https://openalex.org/I121797337"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I121797337"],"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/T11673","display_name":"Advanced Topics in Algebra","score":0.8461999893188477,"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"}},"topics":[{"id":"https://openalex.org/T11673","display_name":"Advanced Topics in Algebra","score":0.8461999893188477,"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/T10287","display_name":"Algebraic structures and combinatorial models","score":0.09300000220537186,"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"}},{"id":"https://openalex.org/T10849","display_name":"Finite Group Theory Research","score":0.038600001484155655,"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/finite-groups","display_name":"finite groups","score":0.5090000033378601},{"id":"https://openalex.org/keywords/group-factorization","display_name":"group factorization","score":0.44699999690055847},{"id":"https://openalex.org/keywords/semisimple-hopf-algebras","display_name":"semisimple Hopf algebras","score":0.890999972820282},{"id":"https://openalex.org/keywords/cosemisimple-hopf-algebras","display_name":"cosemisimple Hopf algebras","score":0.9929999709129333},{"id":"https://openalex.org/keywords/abelian-extensions","display_name":"abelian extensions","score":0.9380000233650208},{"id":"https://openalex.org/keywords/fiber-functors","display_name":"fiber functors","score":0.5199999809265137}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8748999834060669},{"id":"https://openalex.org/C9991821","wikidata":"https://www.wikidata.org/wiki/Q858520","display_name":"Divisibility rule","level":2,"score":0.7653999924659729},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.6216999888420105},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.6193000078201294},{"id":"https://openalex.org/C29712632","wikidata":"https://www.wikidata.org/wiki/Q1627597","display_name":"Hopf algebra","level":3,"score":0.6049000024795532},{"id":"https://openalex.org/C2780388253","wikidata":"https://www.wikidata.org/wiki/Q5421508","display_name":"Exponent","level":2,"score":0.6040999889373779},{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.5914999842643738},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.49939998984336853},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.3894999921321869},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.359499990940094},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3158000111579895},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.30640000104904175},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.2937000095844269},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.27239999175071716},{"id":"https://openalex.org/C118712358","wikidata":"https://www.wikidata.org/wiki/Q782566","display_name":"Automorphism","level":2,"score":0.2632000148296356},{"id":"https://openalex.org/C98184364","wikidata":"https://www.wikidata.org/wiki/Q1780131","display_name":"Argument (complex analysis)","level":2,"score":0.25270000100135803},{"id":"https://openalex.org/C74497983","wikidata":"https://www.wikidata.org/wiki/Q1330788","display_name":"Weierstrass factorization theorem","level":3,"score":0.2502000033855438}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.14972","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.14972","pdf_url":"https://arxiv.org/pdf/2608.14972","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.2608.14972","doi":"https://doi.org/10.48550/arxiv.2608.14972","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.14972","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:2608.14972","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.14972","pdf_url":"https://arxiv.org/pdf/2608.14972","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/W7203708703.pdf","grobid_xml":"https://content.openalex.org/works/W7203708703.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W1538693018"],"related_works":["https://openalex.org/W2964003124","https://openalex.org/W2007466762","https://openalex.org/W2883824802","https://openalex.org/W2028195665","https://openalex.org/W2072418581","https://openalex.org/W2229489885","https://openalex.org/W2400669168","https://openalex.org/W3098073941","https://openalex.org/W3187807205","https://openalex.org/W1968539952"],"abstract_inverted_index":{"Let":[0],"$G=F\u0393$":[1],"be":[2,19],"a":[3,6,35,51,77,111,117],"factorization":[4,113],"of":[5,63],"finite":[7],"group,":[8],"with":[9,15,46],"neither":[10],"factor":[11],"assumed":[12],"normal":[13],"and":[14,50,65,71,127],"$F\\cap\u0393$":[16],"allowed":[17],"to":[18,123],"nontrivial.":[20],"We":[21,120],"prove":[22,55],"that":[23,29],"$\\exp(G)$":[24],"divides":[25,31],"$\\operatorname{lcm}(|F|,|\u0393|)$,":[26],"or":[27],"equivalently":[28],"$\\gcd([G:F],[G:\u0393])\\exp(G)$":[30],"$|G|$.":[32],"This":[33],"answers":[34],"cohomological":[36,92,112],"divisibility":[37,45,93,109],"question":[38],"posed":[39],"by":[40],"Natale.":[41],"Combining":[42],"the":[43,60,89],"group-theoretic":[44],"Natale's":[47],"exponent":[48,57,108],"bound":[49],"lifting":[52],"argument,":[53],"we":[54,104],"Kashina's":[56],"conjecture,":[58],"in":[59,96],"arbitrary-field":[61],"formulation":[62],"Etingof":[64],"Gelaki,":[66],"for":[67,80,94],"every":[68],"finite-dimensional":[69],"semisimple":[70],"cosemisimple":[72],"Hopf":[73,125],"algebra":[74],"$H$":[75],"over":[76],"field":[78],"$k$":[79],"which":[81],"$\\operatorname{Rep}(H\\otimes_k\\overline{k})$":[82],"is":[83],"group-theoretical.":[84],"The":[85],"same":[86],"argument":[87],"proves":[88],"corresponding":[90],"degree-three":[91],"coefficients":[95],"an":[97],"arbitrary":[98],"$G$-module.":[99],"For":[100],"complex":[101],"group-theoretical":[102],"categories,":[103],"also":[105],"establish":[106],"Frobenius-Schur":[107],"under":[110],"hypothesis,":[114],"without":[115],"assuming":[116],"fiber":[118],"functor.":[119],"derive":[121],"applications":[122],"low-dimensional":[124],"algebras":[126],"abelian":[128],"extensions.":[129]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-08-19T00:00:00"}
