{"id":"https://openalex.org/W2036577062","doi":"https://doi.org/10.1305/ndjfl/1093634651","title":"Stable groups, mostly of finite exponent.","display_name":"Stable groups, mostly of finite exponent.","publication_year":1993,"publication_date":"1993-03-01","ids":{"openalex":"https://openalex.org/W2036577062","doi":"https://doi.org/10.1305/ndjfl/1093634651","mag":"2036577062"},"language":"en","primary_location":{"id":"doi:10.1305/ndjfl/1093634651","is_oa":true,"landing_page_url":"https://doi.org/10.1305/ndjfl/1093634651","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-34/issue-2/Stable-groups-mostly-of-finite-exponent/10.1305/ndjfl/1093634651.pdf","source":{"id":"https://openalex.org/S78544662","display_name":"Notre Dame Journal of Formal Logic","issn_l":"0029-4527","issn":["0029-4527","1939-0726"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315698","host_organization_name":"Duke University Press","host_organization_lineage":["https://openalex.org/P4310315698","https://openalex.org/P4310315572"],"host_organization_lineage_names":["Duke University Press","Duke University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Notre Dame Journal of Formal Logic","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-34/issue-2/Stable-groups-mostly-of-finite-exponent/10.1305/ndjfl/1093634651.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5113593194","display_name":"Frank Olaf Wagner","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Frank O. Wagner","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5113593194"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.4954,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.61882748,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"34","issue":"2","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.8970999717712402,"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":0.8970999717712402,"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/exponent","display_name":"Exponent","score":0.7556477189064026},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5593445897102356},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.34403443336486816},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.09571760892868042},{"id":"https://openalex.org/keywords/linguistics","display_name":"Linguistics","score":0.06175383925437927}],"concepts":[{"id":"https://openalex.org/C2780388253","wikidata":"https://www.wikidata.org/wiki/Q5421508","display_name":"Exponent","level":2,"score":0.7556477189064026},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5593445897102356},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.34403443336486816},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.09571760892868042},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.06175383925437927}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1305/ndjfl/1093634651","is_oa":true,"landing_page_url":"https://doi.org/10.1305/ndjfl/1093634651","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-34/issue-2/Stable-groups-mostly-of-finite-exponent/10.1305/ndjfl/1093634651.pdf","source":{"id":"https://openalex.org/S78544662","display_name":"Notre Dame Journal of Formal Logic","issn_l":"0029-4527","issn":["0029-4527","1939-0726"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315698","host_organization_name":"Duke University Press","host_organization_lineage":["https://openalex.org/P4310315698","https://openalex.org/P4310315572"],"host_organization_lineage_names":["Duke University Press","Duke University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Notre Dame Journal of Formal Logic","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.ndjfl/1093634651","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.ndjfl/1093634651","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"}],"best_oa_location":{"id":"doi:10.1305/ndjfl/1093634651","is_oa":true,"landing_page_url":"https://doi.org/10.1305/ndjfl/1093634651","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-34/issue-2/Stable-groups-mostly-of-finite-exponent/10.1305/ndjfl/1093634651.pdf","source":{"id":"https://openalex.org/S78544662","display_name":"Notre Dame Journal of Formal Logic","issn_l":"0029-4527","issn":["0029-4527","1939-0726"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315698","host_organization_name":"Duke University Press","host_organization_lineage":["https://openalex.org/P4310315698","https://openalex.org/P4310315572"],"host_organization_lineage_names":["Duke University Press","Duke University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Notre Dame Journal of Formal Logic","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2036577062.pdf","grobid_xml":"https://content.openalex.org/works/W2036577062.grobid-xml"},"referenced_works_count":16,"referenced_works":["https://openalex.org/W12140614","https://openalex.org/W1972718081","https://openalex.org/W1973713092","https://openalex.org/W1990215191","https://openalex.org/W2032326877","https://openalex.org/W2058425515","https://openalex.org/W2111449076","https://openalex.org/W2553729695","https://openalex.org/W4251179423","https://openalex.org/W4388290447","https://openalex.org/W6600504507","https://openalex.org/W6643388445","https://openalex.org/W6648045190","https://openalex.org/W6676676300","https://openalex.org/W6729984449","https://openalex.org/W6857973918"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2911598644","https://openalex.org/W2142036596"],"abstract_inverted_index":{"We":[0],"prove":[1,61,76],"certain":[2,73],"properties":[3],"of":[4,7,13,39,47,51,57,64,69,83,96,109,134,203,232,239,249,284,313,353,377],"stable":[5,49,84,98],"groups":[6,56],"finite":[8,14,45,52,285,378],"exponent.In":[9],"particular,":[10],"an":[11,36,65,93],"9\u0390-group":[12],"exponent":[15,23,53],"has":[16,22,307,387],"normal-by-finite":[17],"2-Sylow":[18],"subgroups;":[19],"if":[20,115,129,180,205,316,384],"it":[21,32,130],"3":[24],"2\"":[25],"for":[26,174,301],"some":[27,118,338],"n":[28],"<":[29,142,149,207,282],"\u03c9,":[30],"then":[31,163,187,196,220],"is":[33,54,113,117,127,131,144,151,155,165,177,190,244,262,265,273,290,318,350,367,371,382],"nilpotent-byfinite.We":[34],"give":[35],"easy":[37],"proof":[38],"the":[40,62,132,172,245,256,287,311,327,342,351,360],"fact":[41],"that":[42,105,153,179,255,359],"a":[43,48,97,102,106,110,125,138,156,240,297,302,329,373,380],"locally":[44,343],"subgroup":[46,95,107,126,146,202,231,376],"group":[50,99,111,242,381],"nilpotent-by-finite.For":[55],"infinite":[58],"exponent,":[59],"we":[60,75,88,209,226,275],"definability":[63],"algebraically":[66],"closed":[67],"field":[68],"characteristic":[70],"2":[71,293],"under":[72],"circumstances.Finally,":[74],"two":[77],"general":[78],"propositions":[79],"about":[80],"normal":[81,266],"subgroups":[82,136,252,280],"groups.In":[85],"this":[86,333,370],"paper":[87],"shall":[89],"be":[90,199,324,335],"concerned":[91],"with":[92,121,159,247],"arbitrary":[94],"(in":[100],"short:":[101],"substable":[103,182,241],"group).Recall":[104],"H":[108,122,141,150,208,243,248,259,268,272,283,317,332,356,364],"G":[112,143,222,234],"definable":[114,135,167,251,279,331,375],"there":[116,154],"formula":[119,157],"\u03c6(x)":[120,214],"=":[123,161,194],"<p(G);":[124],"typedefinable":[128],"intersection":[133,246,352],"in":[137,267,310,337],"saturated":[139,298],"model.If":[140],"any":[145],"and":[147,183,269,296,300],"K":[148,160,164,206,253,281],"such":[152,254,358],"\u03c6":[158],"\u03c6(H),":[162],"relatively":[166,185,330,374],"(with":[168],"respect":[169],"to":[170,212,326],"//);":[171],"definition":[173],"relative":[175],"type-definability":[176],"analogous.Note":[178],"//is":[181],"K<H":[184],"definable,":[186,274],"also":[188],"H/K":[189,197,229],"substable:":[191],"If":[192],"\u03c6(H)":[193],"K,":[195],"may":[198,210,227,322,334],"viewed":[200],"as":[201,230],"G/\u03c6(G);":[204],"prefer":[211],"replace":[213],"by":[215,340],"\u03c6{\u03c7)":[216],"-\u039bheH\u03a8(x":[217],"h":[218],")>":[219],"N":[221,233],"(\u03c8(G))":[223],">":[224],"//and":[225],"view":[228],"(\u03c8(G))/\\l/(G).The":[235],"connected":[236,305,344],"component":[237,306,345],"H\u00b0":[238,264,321],"all":[250,354],"index":[257,288,361],"IH:":[258],"\u03a0":[260,363],"KI":[261],"finite;":[263],"itself":[270],"connected.If":[271],"need":[276],"only":[277,388],"consider":[278],"index.So":[286],"\\H:H\u00b0\\":[289],"at":[291],"most":[292],"|7":[294],"\u038a":[295],"model":[299],"type-definable":[303],"Hthe":[304],"comparable":[308],"size.But":[309],"absence":[312],"saturation":[314],"or":[315],"just":[319],"substable,":[320],"even":[323],"reduced":[325],"identity!For":[328],"remedied":[336],"cases":[339],"considering":[341],"//":[346],"c":[347],",":[348],"which":[349],"conjugates":[355],"8":[357,365],"\\H:H":[362],"\\":[366],"finite.By":[368],"Baldwin-Saxl,":[369],"again":[372],"index.Finally,":[379],"small":[383],"its":[385],"theory":[386],"countably":[389],"many":[390],"pure":[391],"types.":[392]},"counts_by_year":[],"updated_date":"2026-08-08T01:25:22.217667","created_date":"2025-10-10T00:00:00"}
