{"id":"https://openalex.org/W1982209059","doi":"https://doi.org/10.2178/jsl/1231082300","title":"Normal subgroups of infinite symmetric groups, with an application to stratified set theory","display_name":"Normal subgroups of infinite symmetric groups, with an application to stratified set theory","publication_year":2009,"publication_date":"2009-01-04","ids":{"openalex":"https://openalex.org/W1982209059","doi":"https://doi.org/10.2178/jsl/1231082300","mag":"1982209059"},"language":"en","primary_location":{"id":"doi:10.2178/jsl/1231082300","is_oa":false,"landing_page_url":"https://doi.org/10.2178/jsl/1231082300","pdf_url":null,"source":{"id":"https://openalex.org/S177675236","display_name":"Journal of Symbolic Logic","issn_l":"0022-4812","issn":["0022-4812","1943-5886"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Journal of Symbolic Logic","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/A5112266022","display_name":"Nathan Bowler","orcid":null},"institutions":[{"id":"https://openalex.org/I4210153325","display_name":"Institute of Mathematical Statistics","ror":"https://ror.org/043f04882","country_code":"US","type":"other","lineage":["https://openalex.org/I4210153325"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Nathan Bowler","raw_affiliation_strings":["Department of Pure Mathematics and Mathematical Statistics, Centre for Mathematical Sciences, Wilberforce Road, Cambridge Cb3 0Wb, United Kingdom, E-mail:"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Pure Mathematics and Mathematical Statistics, Centre for Mathematical Sciences, Wilberforce Road, Cambridge Cb3 0Wb, United Kingdom, E-mail:","institution_ids":["https://openalex.org/I4210153325"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5006033525","display_name":"Thomas F\u00f6rster","orcid":"https://orcid.org/0000-0002-7711-2276"},"institutions":[{"id":"https://openalex.org/I4210153325","display_name":"Institute of Mathematical Statistics","ror":"https://ror.org/043f04882","country_code":"US","type":"other","lineage":["https://openalex.org/I4210153325"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Thomas Forster","raw_affiliation_strings":["Department of Pure Mathematics and Mathematical Statistics, Centre for Mathematical Sciences, Wilberforce Road, Cambridge Cb3 0Wb, United Kingdom, E-mail:"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Pure Mathematics and Mathematical Statistics, Centre for Mathematical Sciences, Wilberforce Road, Cambridge Cb3 0Wb, United Kingdom, E-mail:","institution_ids":["https://openalex.org/I4210153325"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I4210153325"],"apc_list":null,"apc_paid":null,"fwci":0.7575,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.66167692,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"74","issue":"1","first_page":"17","last_page":"26"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9692000150680542,"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"}},"topics":[{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9692000150680542,"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":0.9039999842643738,"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/permutation","display_name":"Permutation (music)","score":0.7991981506347656},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.74930739402771},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7466318607330322},{"id":"https://openalex.org/keywords/permutation-group","display_name":"Permutation group","score":0.6763826012611389},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.6499091386795044},{"id":"https://openalex.org/keywords/symmetric-group","display_name":"Symmetric group","score":0.645809531211853},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.559764564037323},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.518418550491333},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.49118277430534363},{"id":"https://openalex.org/keywords/normal-subgroup","display_name":"Normal subgroup","score":0.49015721678733826},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.4844989478588104},{"id":"https://openalex.org/keywords/axiom-of-choice","display_name":"Axiom of choice","score":0.41600868105888367},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.41200998425483704},{"id":"https://openalex.org/keywords/set-theory","display_name":"Set theory","score":0.34263575077056885},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.06846979260444641},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06513959169387817},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.05751436948776245}],"concepts":[{"id":"https://openalex.org/C21308566","wikidata":"https://www.wikidata.org/wiki/Q7169365","display_name":"Permutation (music)","level":2,"score":0.7991981506347656},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.74930739402771},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7466318607330322},{"id":"https://openalex.org/C92957085","wikidata":"https://www.wikidata.org/wiki/Q1412905","display_name":"Permutation group","level":3,"score":0.6763826012611389},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.6499091386795044},{"id":"https://openalex.org/C128622974","wikidata":"https://www.wikidata.org/wiki/Q849512","display_name":"Symmetric group","level":2,"score":0.645809531211853},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.559764564037323},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.518418550491333},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.49118277430534363},{"id":"https://openalex.org/C105515060","wikidata":"https://www.wikidata.org/wiki/Q743179","display_name":"Normal subgroup","level":3,"score":0.49015721678733826},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.4844989478588104},{"id":"https://openalex.org/C151797676","wikidata":"https://www.wikidata.org/wiki/Q179692","display_name":"Axiom of choice","level":4,"score":0.41600868105888367},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.41200998425483704},{"id":"https://openalex.org/C153046414","wikidata":"https://www.wikidata.org/wiki/Q12482","display_name":"Set theory","level":3,"score":0.34263575077056885},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.06846979260444641},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06513959169387817},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.05751436948776245},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.2178/jsl/1231082300","is_oa":false,"landing_page_url":"https://doi.org/10.2178/jsl/1231082300","pdf_url":null,"source":{"id":"https://openalex.org/S177675236","display_name":"Journal of Symbolic Logic","issn_l":"0022-4812","issn":["0022-4812","1943-5886"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Journal of Symbolic Logic","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.jsl/1231082300","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1231082300","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"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":"","raw_type":"Text"},{"id":"pmh:oai:ueaeprints.uea.ac.uk:10186","is_oa":false,"landing_page_url":"https://ueaeprints.uea.ac.uk/id/eprint/10186/","pdf_url":null,"source":{"id":"https://openalex.org/S4306400384","display_name":"UEA Digital Repository (University of East Anglia)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1118541","host_organization_name":"University of East Anglia","host_organization_lineage":["https://openalex.org/I1118541"],"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":"Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":3,"referenced_works":["https://openalex.org/W1989782859","https://openalex.org/W2085194630","https://openalex.org/W4241164520"],"related_works":["https://openalex.org/W1574825745","https://openalex.org/W2151251236","https://openalex.org/W131839596","https://openalex.org/W3133665497","https://openalex.org/W3013480779","https://openalex.org/W4292719633","https://openalex.org/W2950405155","https://openalex.org/W338933924","https://openalex.org/W4300591056","https://openalex.org/W2070408914"],"abstract_inverted_index":{"It":[0],"is":[1,70,74,104,124,134,174],"generally":[2],"known":[3],"that":[4,71,188,214],"infinite":[5,76],"symmetric":[6],"groups":[7],"have":[8,55],"few":[9],"nontrivial":[10,94],"normal":[11,95,190],"subgroups":[12,16,96],"(typically":[13],"only":[14],"the":[15,37,43,60,108,165,215],"of":[17,22,45,49,52,62,97,107,110,127,160,167,172,192],"bounded":[18],"support)":[19],"and":[20],"none":[21],"small":[23,34,98,197],"index.":[24,99],"(We":[25],"will":[26,205],"explain":[27],"later":[28],"exactly":[29],"what":[30],"we":[31,54,163,186,210],"mean":[32],"by":[33],").":[35,221],"However":[36],"standard":[38],"analysis":[39],"relies":[40],"heavily":[41],"on":[42],"axiom":[44,61],"choice.":[46,63],"By":[47],"dint":[48],"a":[50,125,135,156],"lot":[51],"combinatorics":[53],"been":[56],"able":[57],"to":[58,145],"dispense\u2014largely\u2014with":[59],"Largely,":[64],"but":[65],"not":[66],"entirely:":[67],"our":[68],"result":[69],"if":[72,176],"X":[73,80,84,86,90,137,140,142,173,182,194,220],"an":[75],"set":[77,136],"with":[78,138],"\u2223":[79,81,83,87,181],"=":[82],"\u00d7":[85],"then":[88],"Symm(":[89,139,193,219],")":[91,143,195],"has":[92],"no":[93],"Some":[100],"condition":[101],"like":[102],"this":[103],"needed":[105],"because":[106],"work":[109],"Sam":[111],"Tarzi":[112],"who":[113],"showed":[114],"[4]":[115],"that,":[116],"for":[117],"any":[118],"finite":[119],"group":[120],"G":[121,146],",":[122],"there":[123,133],"model":[126],"ZF":[128],"without":[129],"AC":[130],"in":[131,151],"which":[132,162],")/FSymm(":[141],"isomorphic":[144],".":[147],"The":[148],"proof":[149],"proceeds":[150],"two":[152],"stages.":[153],"We":[154],"consider":[155],"particularly":[157],"useful":[158],"class":[159,166],"permutations,":[161],"call":[164],"flexible":[168,175,202,216],"permutations.":[169],"A":[170],"permutation":[171],"it":[177],"fixes":[178],"at":[179],"least":[180],"\u2223-many":[183],"points.":[184],"First":[185],"show":[187,211],"every":[189,201],"subgroup":[191],"(of":[196],"index)":[198],"must":[199],"contain":[200],"permutation.":[203],"This":[204],"be":[206],"theorem":[207],"4.":[208],"Then":[209],"(theorem":[212],"7)":[213],"permutations":[217],"generate":[218]},"counts_by_year":[{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
