{"id":"https://openalex.org/W7225200043","doi":"https://doi.org/10.48550/arxiv.2611.02608","title":"A note on an extension of Shidov's theorem and Shlyk's theorem","display_name":"A note on an extension of Shidov's theorem and Shlyk's theorem","publication_year":2026,"publication_date":"2026-11-02","ids":{"openalex":"https://openalex.org/W7225200043","doi":"https://doi.org/10.48550/arxiv.2611.02608"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2611.02608","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2611.02608","pdf_url":"https://arxiv.org/pdf/2611.02608","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/2611.02608","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5016981451","display_name":"Jiangtao Shi","orcid":"https://orcid.org/0000-0003-3092-280X","observed_orcids":["https://orcid.org/0000-0003-3092-280X"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Shi, Jiangtao","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5101812993","display_name":"Fanghua Li","orcid":"https://orcid.org/0000-0002-7696-6106","observed_orcids":["https://orcid.org/0000-0002-7696-6106","https://orcid.org/0009-0005-7084-860X"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Li, Fanghua","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"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/2610","display_name":"Mathematical Physics"},"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/T12504","display_name":"Mathematics and Applications","score":0.0,"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/non-solvable-groups","display_name":"non-solvable groups","score":0.9769999980926514},{"id":"https://openalex.org/keywords/sylow-subgroups","display_name":"Sylow subgroups","score":0.878000020980835},{"id":"https://openalex.org/keywords/normalizers","display_name":"normalizers","score":0.75},{"id":"https://openalex.org/keywords/intersection-of-subgroups","display_name":"intersection of subgroups","score":0.718999981880188},{"id":"https://openalex.org/keywords/finite-groups","display_name":"finite groups","score":0.47600001096725464}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8744999766349792},{"id":"https://openalex.org/C146147875","wikidata":"https://www.wikidata.org/wiki/Q1144897","display_name":"Brouwer fixed-point theorem","level":3,"score":0.5378000140190125},{"id":"https://openalex.org/C119050217","wikidata":"https://www.wikidata.org/wiki/Q17101806","display_name":"Intersection theorem","level":5,"score":0.5281000137329102},{"id":"https://openalex.org/C124535231","wikidata":"https://www.wikidata.org/wiki/Q1057919","display_name":"Sylow theorems","level":4,"score":0.5220999717712402},{"id":"https://openalex.org/C86115822","wikidata":"https://www.wikidata.org/wiki/Q6086104","display_name":"Isomorphism extension theorem","level":4,"score":0.5134999752044678},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5097000002861023},{"id":"https://openalex.org/C75174853","wikidata":"https://www.wikidata.org/wiki/Q190629","display_name":"Centralizer and normalizer","level":2,"score":0.4837999939918518},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.47749999165534973},{"id":"https://openalex.org/C2776230367","wikidata":"https://www.wikidata.org/wiki/Q7314222","display_name":"Representation theorem","level":2,"score":0.4740999937057495},{"id":"https://openalex.org/C45962547","wikidata":"https://www.wikidata.org/wiki/Q1422068","display_name":"Fixed-point theorem","level":2,"score":0.4587000012397766},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.4519999921321869},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.446399986743927},{"id":"https://openalex.org/C90985795","wikidata":"https://www.wikidata.org/wiki/Q5042898","display_name":"Carlson's theorem","level":5,"score":0.4178999960422516},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.3952000141143799},{"id":"https://openalex.org/C194886279","wikidata":"https://www.wikidata.org/wiki/Q430271","display_name":"Fundamental theorem","level":3,"score":0.3831999897956848},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.3801000118255615},{"id":"https://openalex.org/C171636804","wikidata":"https://www.wikidata.org/wiki/Q1149458","display_name":"Compactness theorem","level":4,"score":0.3700000047683716},{"id":"https://openalex.org/C48540410","wikidata":"https://www.wikidata.org/wiki/Q5221089","display_name":"Danskin's theorem","level":4,"score":0.36899998784065247},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.33340001106262207},{"id":"https://openalex.org/C206929604","wikidata":"https://www.wikidata.org/wiki/Q530152","display_name":"Picard\u2013Lindel\u00f6f theorem","level":3,"score":0.3255000114440918},{"id":"https://openalex.org/C203492994","wikidata":"https://www.wikidata.org/wiki/Q909669","display_name":"Divisor (algebraic geometry)","level":2,"score":0.31279999017715454},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2955000102519989},{"id":"https://openalex.org/C30860621","wikidata":"https://www.wikidata.org/wiki/Q49008","display_name":"Prime factor","level":3,"score":0.2872999906539917},{"id":"https://openalex.org/C26231708","wikidata":"https://www.wikidata.org/wiki/Q1065966","display_name":"Isomorphism theorem","level":2,"score":0.28700000047683716},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.28049999475479126},{"id":"https://openalex.org/C139588767","wikidata":"https://www.wikidata.org/wiki/Q17098096","display_name":"Mean value theorem (divided differences)","level":4,"score":0.2687999904155731},{"id":"https://openalex.org/C200116569","wikidata":"https://www.wikidata.org/wiki/Q902052","display_name":"G\u00f6del's completeness theorem","level":2,"score":0.2630000114440918},{"id":"https://openalex.org/C40429337","wikidata":"https://www.wikidata.org/wiki/Q1108687","display_name":"Factor theorem","level":4,"score":0.26080000400543213}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2611.02608","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2611.02608","pdf_url":"https://arxiv.org/pdf/2611.02608","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.2611.02608","doi":"https://doi.org/10.48550/arxiv.2611.02608","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2611.02608","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","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2611.02608","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2611.02608","pdf_url":"https://arxiv.org/pdf/2611.02608","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7202241794","https://openalex.org/W7225169623","https://openalex.org/W2376273686","https://openalex.org/W2379521135","https://openalex.org/W1998794096","https://openalex.org/W2051871869","https://openalex.org/W4226317217","https://openalex.org/W4245531954","https://openalex.org/W2121290777","https://openalex.org/W4321791807"],"abstract_inverted_index":{"Let":[0],"$G$":[1,25],"be":[2],"a":[3,42],"non-solvable":[4],"group":[5],"and":[6,48],"$p$":[7,30],"any":[8],"fixed":[9],"prime":[10],"divisor":[11],"of":[12,19,24,26,34,45],"$|G|$.":[13],"We":[14],"prove":[15],"that":[16],"the":[17,32],"intersection":[18],"all":[20],"non-nilpotent":[21],"maximal":[22],"subgroups":[23],"order":[27],"divisible":[28],"by":[29],"containing":[31],"normalizer":[33],"some":[35],"Sylow":[36],"subgroup":[37],"is":[38],"$p$-closed,":[39],"which":[40],"provides":[41],"further":[43],"generalization":[44],"Shidov's":[46],"theorem":[47],"Shlyk's":[49],"theorem.":[50]},"counts_by_year":[],"updated_date":"2026-11-05T12:25:35.769452","created_date":"2026-11-04T00:00:00"}
