{"id":"https://openalex.org/W4410892291","doi":"https://doi.org/10.1142/s0218196725500237","title":"Base sizes for finite unitary and symplectic groups with solvable stabilisers","display_name":"Base sizes for finite unitary and symplectic groups with solvable stabilisers","publication_year":2025,"publication_date":"2025-05-30","ids":{"openalex":"https://openalex.org/W4410892291","doi":"https://doi.org/10.1142/s0218196725500237"},"language":"en","primary_location":{"id":"doi:10.1142/s0218196725500237","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196725500237","pdf_url":null,"source":{"id":"https://openalex.org/S23260266","display_name":"International Journal of Algebra and Computation","issn_l":"0218-1967","issn":["0218-1967","1793-6500"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Algebra and Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5064183904","display_name":"Anton A. Baykalov","orcid":"https://orcid.org/0000-0003-2926-6737"},"institutions":[{"id":"https://openalex.org/I188760350","display_name":"Ollscoil na Gaillimhe \u2013 University of Galway","ror":"https://ror.org/03bea9k73","country_code":"IE","type":"education","lineage":["https://openalex.org/I188760350"]}],"countries":["IE"],"is_corresponding":true,"raw_author_name":"Anton A. Baykalov","raw_affiliation_strings":["School of Mathematical and Statistical Sciences, University of Galway, Galway, Ireland"],"raw_orcid":"https://orcid.org/0000-0003-2926-6737","affiliations":[{"raw_affiliation_string":"School of Mathematical and Statistical Sciences, University of Galway, Galway, Ireland","institution_ids":["https://openalex.org/I188760350"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5064183904"],"corresponding_institution_ids":["https://openalex.org/I188760350"],"apc_list":null,"apc_paid":null,"fwci":9.0414,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.97407698,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":99},"biblio":{"volume":"35","issue":"06","first_page":"823","last_page":"908"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10849","display_name":"Finite Group Theory Research","score":0.9998999834060669,"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":0.9998999834060669,"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/T10304","display_name":"Geometric and Algebraic Topology","score":0.9976999759674072,"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/T11130","display_name":"Coding theory and cryptography","score":0.996999979019165,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.9156471490859985},{"id":"https://openalex.org/keywords/unitary-state","display_name":"Unitary state","score":0.7987425923347473},{"id":"https://openalex.org/keywords/symplectic-geometry","display_name":"Symplectic geometry","score":0.7606428265571594},{"id":"https://openalex.org/keywords/base","display_name":"Base (topology)","score":0.5675745606422424},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5235052704811096},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4218764901161194},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.16485309600830078}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9156471490859985},{"id":"https://openalex.org/C67820243","wikidata":"https://www.wikidata.org/wiki/Q179164","display_name":"Unitary state","level":2,"score":0.7987425923347473},{"id":"https://openalex.org/C168619227","wikidata":"https://www.wikidata.org/wiki/Q2190991","display_name":"Symplectic geometry","level":2,"score":0.7606428265571594},{"id":"https://openalex.org/C42058472","wikidata":"https://www.wikidata.org/wiki/Q810214","display_name":"Base (topology)","level":2,"score":0.5675745606422424},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5235052704811096},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4218764901161194},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.16485309600830078},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218196725500237","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196725500237","pdf_url":null,"source":{"id":"https://openalex.org/S23260266","display_name":"International Journal of Algebra and Computation","issn_l":"0218-1967","issn":["0218-1967","1793-6500"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Algebra and Computation","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W412431710","https://openalex.org/W656473322","https://openalex.org/W1490644506","https://openalex.org/W1493654001","https://openalex.org/W1565081156","https://openalex.org/W1567200859","https://openalex.org/W1649227877","https://openalex.org/W1964582653","https://openalex.org/W1976677460","https://openalex.org/W1981477383","https://openalex.org/W1991192224","https://openalex.org/W1999060257","https://openalex.org/W2005832340","https://openalex.org/W2031685413","https://openalex.org/W2057680076","https://openalex.org/W2067068899","https://openalex.org/W2099901768","https://openalex.org/W2122198415","https://openalex.org/W2147813260","https://openalex.org/W2148757468","https://openalex.org/W2196559987","https://openalex.org/W2490728539","https://openalex.org/W2736249634","https://openalex.org/W3106220820","https://openalex.org/W3125988253","https://openalex.org/W3157502088","https://openalex.org/W4206451259","https://openalex.org/W4213333252","https://openalex.org/W4235578156","https://openalex.org/W4253689595","https://openalex.org/W4401009976","https://openalex.org/W4407677712"],"related_works":["https://openalex.org/W2187058597","https://openalex.org/W1972361952","https://openalex.org/W4297967242","https://openalex.org/W4385970320","https://openalex.org/W2021613246","https://openalex.org/W2769537058","https://openalex.org/W4301808655","https://openalex.org/W2522170085","https://openalex.org/W2973399580","https://openalex.org/W2050868116"],"abstract_inverted_index":{"Let":[0],"G":[1,22,34,58],"be":[2],"a":[3,8,99],"transitive":[4],"permutation":[5],"group":[6],"on":[7],"finite":[9],"set":[10],"with":[11,109,127],"solvable":[12,19],"point":[13],"stabiliser":[14],"and":[15,64,73,134],"assume":[16],"that":[17,29],"the":[18,30,55,77,81,85,94,103,143,154],"radical":[20],"of":[21,33,68,80,87,102,156],"is":[23,35,59,76],"trivial.":[24],"In":[25,93,116],"2010,":[26],"Vdovin":[27,51],"conjectured":[28],"base":[31],"size":[32],"at":[36],"most":[37],"5.":[38],"Burness":[39],"proved":[40],"this":[41,117,121],"conjecture":[42,89,104,144,158],"for":[43,90,105,145,159],"primitive":[44],"G.":[45],"The":[46,138],"problem":[47],"was":[48],"reduced":[49,65],"by":[50,71],"in":[52],"2012":[53],"to":[54,66,84,112,123,130],"case":[56],"when":[57],"an":[60],"almost":[61,106,124,161],"simple":[62,107,125,162],"group,":[63],"groups":[67,108,126],"Lie":[69],"type":[70],"Baykalov":[72],"Burness.":[74],"This":[75],"second":[78],"paper":[79,140,151],"series":[82],"devoted":[83],"study":[86],"Vdovin\u2019s":[88,157],"classical":[91,163],"groups.":[92,147,164],"first":[95],"paper,":[96,118],"we":[97,119],"prove":[98],"strong":[100],"form":[101],"socle":[110,128],"isomorphic":[111,129],"[Formula:":[113,131,135],"see":[114,132,136],"text]":[115,133,137],"extend":[120],"result":[122],"final":[139],"will":[141,152],"establish":[142],"orthogonal":[146],"Together,":[148],"these":[149],"three":[150],"complete":[153],"proof":[155],"all":[160]},"counts_by_year":[{"year":2026,"cited_by_count":2}],"updated_date":"2026-05-21T09:19:25.381259","created_date":"2025-10-10T00:00:00"}