{"id":"https://openalex.org/W7204802392","doi":"https://doi.org/10.48550/arxiv.2608.27525","title":"Orbits of submaximal dimension for Sylow $p$-subgroups of finite classical orthogonal groups","display_name":"Orbits of submaximal dimension for Sylow $p$-subgroups of finite classical orthogonal groups","publication_year":2026,"publication_date":"2026-08-27","ids":{"openalex":"https://openalex.org/W7204802392","doi":"https://doi.org/10.48550/arxiv.2608.27525"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.27525","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.27525","pdf_url":"https://arxiv.org/pdf/2608.27525","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/2608.27525","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5050317472","display_name":"Mikhail V. Ignatev","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I118501908","display_name":"National Research University Higher School of Economics","ror":"https://ror.org/055f7t516","country_code":"RU","type":"education","lineage":["https://openalex.org/I118501908"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Ignatev, Mikhail","raw_affiliation_strings":["Mikhail Ignatev : National Research University Higher School of Economics , Pokrovsky Boulevard 11 , 109028 , Moscow , Russia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mikhail Ignatev : National Research University Higher School of Economics , Pokrovsky Boulevard 11 , 109028 , Moscow , Russia","institution_ids":["https://openalex.org/I118501908"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5093096232","display_name":"Mikhail Venchakov","orcid":"https://orcid.org/0000-0002-5326-1023","observed_orcids":["https://orcid.org/0000-0002-5326-1023"]},"institutions":[{"id":"https://openalex.org/I118501908","display_name":"National Research University Higher School of Economics","ror":"https://ror.org/055f7t516","country_code":"RU","type":"education","lineage":["https://openalex.org/I118501908"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Venchakov, Mikhail","raw_affiliation_strings":["National Research University Higher School of Economics , Pokrovsky Boulevard 11 , 109028 , Moscow , Russia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"National Research University Higher School of Economics , Pokrovsky Boulevard 11 , 109028 , Moscow , Russia","institution_ids":["https://openalex.org/I118501908"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I118501908"],"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":0.9976000189781189,"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":0.9976000189781189,"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":0.002300000051036477,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.00019999999494757503,"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/sylow-p-subgroups","display_name":"Sylow p-subgroups","score":0.968999981880188},{"id":"https://openalex.org/keywords/coadjoint-orbits","display_name":"coadjoint orbits","score":0.9150000214576721},{"id":"https://openalex.org/keywords/irreducible-complex-characters","display_name":"irreducible complex characters","score":0.7820000052452087},{"id":"https://openalex.org/keywords/finite-fields","display_name":"finite fields","score":0.49900001287460327},{"id":"https://openalex.org/keywords/orbit-counting","display_name":"orbit counting","score":0.4009999930858612}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7924000024795532},{"id":"https://openalex.org/C124535231","wikidata":"https://www.wikidata.org/wiki/Q1057919","display_name":"Sylow theorems","level":4,"score":0.733299970626831},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.6470000147819519},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.5733000040054321},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5260000228881836},{"id":"https://openalex.org/C35661339","wikidata":"https://www.wikidata.org/wiki/Q2285809","display_name":"Classical group","level":3,"score":0.5231000185012817},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5097000002861023},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.4846999943256378},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.4438999891281128},{"id":"https://openalex.org/C2777404646","wikidata":"https://www.wikidata.org/wiki/Q1057968","display_name":"Finite group","level":3,"score":0.43529999256134033},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.4316999912261963},{"id":"https://openalex.org/C112313634","wikidata":"https://www.wikidata.org/wiki/Q7886648","display_name":"Complement (music)","level":5,"score":0.4117000102996826},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3935999870300293},{"id":"https://openalex.org/C42321380","wikidata":"https://www.wikidata.org/wiki/Q849705","display_name":"Characteristic polynomial","level":3,"score":0.32829999923706055},{"id":"https://openalex.org/C196644772","wikidata":"https://www.wikidata.org/wiki/Q3884964","display_name":"Orbit (dynamics)","level":2,"score":0.3208000063896179},{"id":"https://openalex.org/C146561895","wikidata":"https://www.wikidata.org/wiki/Q1783179","display_name":"Orthogonal group","level":2,"score":0.3093999922275543},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.30399999022483826},{"id":"https://openalex.org/C172331165","wikidata":"https://www.wikidata.org/wiki/Q524607","display_name":"General linear group","level":3,"score":0.2888000011444092},{"id":"https://openalex.org/C81651864","wikidata":"https://www.wikidata.org/wiki/Q874429","display_name":"Group theory","level":2,"score":0.2847000062465668},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.27379998564720154},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.25940001010894775},{"id":"https://openalex.org/C168167062","wikidata":"https://www.wikidata.org/wiki/Q1117970","display_name":"Component (thermodynamics)","level":2,"score":0.2531000077724457}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.27525","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.27525","pdf_url":"https://arxiv.org/pdf/2608.27525","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.2608.27525","doi":"https://doi.org/10.48550/arxiv.2608.27525","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.27525","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:2608.27525","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.27525","pdf_url":"https://arxiv.org/pdf/2608.27525","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/G4658241017","display_name":null,"funder_award_id":"25-21-00219","funder_id":"https://openalex.org/F4320324099","funder_display_name":"Russian Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320324099","display_name":"Russian Science Foundation","ror":"https://ror.org/03y2gwe85"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7204802392.pdf","grobid_xml":"https://content.openalex.org/works/W7204802392.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7204819284","https://openalex.org/W7133839571","https://openalex.org/W4399510467","https://openalex.org/W2011326531","https://openalex.org/W2141665995","https://openalex.org/W1977130743","https://openalex.org/W7130010170","https://openalex.org/W2025792512","https://openalex.org/W1639830652","https://openalex.org/W2964333459"],"abstract_inverted_index":{"Let":[0],"$U$":[1,29],"be":[2],"a":[3,7,12,48,57,77],"Sylow":[4],"$p$-subgroup":[5],"in":[6,34,79],"classical":[8],"orthogonal":[9],"group":[10,28],"over":[11],"finite":[13],"field":[14],"with":[15,83,89],"$q$":[16],"elements":[17],"of":[18,26,37,41,50,53,63,73],"characteristic":[19],"$p$":[20],"large":[21],"enough.":[22],"The":[23],"coadjoint":[24],"orbits":[25,52,65],"the":[27,31,35,44,61,90],"play":[30],"key":[32],"role":[33],"description":[36],"irreducible":[38],"complex":[39],"characters":[40],"$U$.":[42],"In":[43],"paper,":[45],"we":[46,59],"provide":[47],"classification":[49],"such":[51],"pre-maximal":[54],"dimension.":[55],"As":[56],"corollary,":[58],"compute":[60],"number":[62],"all":[64],"mentioned":[66],"above.":[67],"It":[68],"turned":[69],"out":[70],"that":[71],"each":[72],"these":[74],"numbers":[75],"is":[76],"polynomial":[78],"$q":[80],"-":[81],"1$":[82],"integer":[84],"non-negative":[85],"coefficients,":[86],"which":[87],"agrees":[88],"Isaacs'":[91],"conjecture.":[92]},"counts_by_year":[],"updated_date":"2026-11-06T12:05:46.655746","created_date":"2026-09-01T00:00:00"}