{"id":"https://openalex.org/W2021683857","doi":"https://doi.org/10.1142/s0218196712500324","title":"GROUPS IN WHICH THE NORMAL CLOSURES OF CYCLIC SUBGROUPS HAVE FINITE SECTION RANK","display_name":"GROUPS IN WHICH THE NORMAL CLOSURES OF CYCLIC SUBGROUPS HAVE FINITE SECTION RANK","publication_year":2012,"publication_date":"2012-02-05","ids":{"openalex":"https://openalex.org/W2021683857","doi":"https://doi.org/10.1142/s0218196712500324","mag":"2021683857"},"language":"en","primary_location":{"id":"doi:10.1142/s0218196712500324","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196712500324","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/A5042417434","display_name":"Leonid A. Kurdachenko","orcid":"https://orcid.org/0000-0002-6368-7319"},"institutions":[{"id":"https://openalex.org/I883679329","display_name":"Oles Honchar Dnipro National University","ror":"https://ror.org/00qk1f078","country_code":"UA","type":"education","lineage":["https://openalex.org/I883679329"]}],"countries":["UA"],"is_corresponding":true,"raw_author_name":"LEONID A. KURDACHENKO","raw_affiliation_strings":["Department of Algebra, National University of Dnepropetrovsk, Vul. Naukova 13, Dnepropetrvsk 50, 49050, Ukraine"],"affiliations":[{"raw_affiliation_string":"Department of Algebra, National University of Dnepropetrovsk, Vul. Naukova 13, Dnepropetrvsk 50, 49050, Ukraine","institution_ids":["https://openalex.org/I883679329"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065401374","display_name":"Jos\u00e9 Mar\u00eda Mu\u00f1oz Escolano","orcid":"https://orcid.org/0000-0002-8713-4591"},"institutions":[{"id":"https://openalex.org/I255234318","display_name":"Universidad de Zaragoza","ror":"https://ror.org/012a91z28","country_code":"ES","type":"education","lineage":["https://openalex.org/I255234318"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"JOS\u00c9 M. MU\u00d1OZ-ESCOLANO","raw_affiliation_strings":["Department of Mathematics, University of Zaragoza, Pedro Cerbuna 12, 50009 Zaragoza, Spain"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Zaragoza, Pedro Cerbuna 12, 50009 Zaragoza, Spain","institution_ids":["https://openalex.org/I255234318"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5041231929","display_name":"Javier Otal","orcid":null},"institutions":[{"id":"https://openalex.org/I255234318","display_name":"Universidad de Zaragoza","ror":"https://ror.org/012a91z28","country_code":"ES","type":"education","lineage":["https://openalex.org/I255234318"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"JAVIER OTAL","raw_affiliation_strings":["Department of Mathematics, University of Zaragoza, Pedro Cerbuna 12, 50009 Zaragoza, Spain"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Zaragoza, Pedro Cerbuna 12, 50009 Zaragoza, Spain","institution_ids":["https://openalex.org/I255234318"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5042417434"],"corresponding_institution_ids":["https://openalex.org/I883679329"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.10661108,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"22","issue":"04","first_page":"1250032","last_page":"1250032"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10849","display_name":"Finite Group Theory Research","score":0.9980000257492065,"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":0.9980000257492065,"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/T11703","display_name":"Rings, Modules, and Algebras","score":0.9315999746322632,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8840339183807373},{"id":"https://openalex.org/keywords/section","display_name":"Section (typography)","score":0.7751083374023438},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.7359936833381653},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7195033431053162},{"id":"https://openalex.org/keywords/abelian-group","display_name":"Abelian group","score":0.679958701133728},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.6776225566864014},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.5449617505073547},{"id":"https://openalex.org/keywords/normal-subgroup","display_name":"Normal subgroup","score":0.5420014262199402},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5204172730445862},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.5169674754142761},{"id":"https://openalex.org/keywords/finite-group","display_name":"Finite group","score":0.4363698959350586},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09627711772918701},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.050310105085372925}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8840339183807373},{"id":"https://openalex.org/C2780129039","wikidata":"https://www.wikidata.org/wiki/Q1931107","display_name":"Section (typography)","level":2,"score":0.7751083374023438},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.7359936833381653},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7195033431053162},{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.679958701133728},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6776225566864014},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.5449617505073547},{"id":"https://openalex.org/C105515060","wikidata":"https://www.wikidata.org/wiki/Q743179","display_name":"Normal subgroup","level":3,"score":0.5420014262199402},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5204172730445862},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.5169674754142761},{"id":"https://openalex.org/C2777404646","wikidata":"https://www.wikidata.org/wiki/Q1057968","display_name":"Finite group","level":3,"score":0.4363698959350586},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09627711772918701},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.050310105085372925},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C112698675","wikidata":"https://www.wikidata.org/wiki/Q37038","display_name":"Advertising","level":1,"score":0.0},{"id":"https://openalex.org/C144133560","wikidata":"https://www.wikidata.org/wiki/Q4830453","display_name":"Business","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","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":1,"locations":[{"id":"doi:10.1142/s0218196712500324","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196712500324","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":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320320719","display_name":"Department of Science and Technology, Ministry of Science and Technology, India","ror":"https://ror.org/0101xrq71"},{"id":"https://openalex.org/F4320322930","display_name":"Ministerio de Ciencia e Innovaci\u00f3n","ror":"https://ror.org/034900433"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W195788117","https://openalex.org/W591591544","https://openalex.org/W646029128","https://openalex.org/W657014803","https://openalex.org/W1566117369","https://openalex.org/W1967261382","https://openalex.org/W2007311477","https://openalex.org/W2020615091","https://openalex.org/W2027877209","https://openalex.org/W2042740070","https://openalex.org/W2047818939","https://openalex.org/W2050881045","https://openalex.org/W2314139063","https://openalex.org/W2325945350","https://openalex.org/W2327630508","https://openalex.org/W2369978792","https://openalex.org/W2490728539","https://openalex.org/W4249405967","https://openalex.org/W4299467763","https://openalex.org/W4300694375","https://openalex.org/W6600363392","https://openalex.org/W6830758940"],"related_works":["https://openalex.org/W4226339964","https://openalex.org/W3217118196","https://openalex.org/W2056660543","https://openalex.org/W3125289115","https://openalex.org/W2157282010","https://openalex.org/W2392384401","https://openalex.org/W2050009095","https://openalex.org/W1979351863","https://openalex.org/W4231882720","https://openalex.org/W3139171162"],"abstract_inverted_index":{"A":[0],"group":[1,75,105],"G":[2,26,44,76,99,116],"is":[3,16,27,37,54,68,100,137],"said":[4],"to":[5,154],"have":[6,117],"finite":[7,28,118],"section":[8,79,120,128],"p-rankr":[9],"p":[10,15,33,49,83,89],"(G)":[11,84],"=":[12,48],"r":[13,34,50,82],"(here":[14],"a":[17,69,74,101,138],"prime)":[18],"if":[19,81,98],"every":[20],"elementary":[21,39],"abelian":[22,40],"p-section":[23,41],"U/V":[24],"of":[25,29,43,57,111,115,141],"order":[30],"at":[31],"most":[32],"and":[35,60,147],"there":[36],"an":[38],"A/B":[42],"such":[45],"that":[46,73,97],"|A/B|":[47],".":[51],"If":[52],"\u2119":[53,63],"the":[55,108,112,159],"set":[56],"all":[58],"primes":[59],"\u03bb":[61],":":[62],"\u2192":[64],"\u2115":[65],"\u222a":[66],"{0}":[67],"function,":[70],"we":[71,95,151],"say":[72],"has":[77,124],"\u03bb-bounded":[78,119],"rank":[80,129],"\u2264":[85],"\u03bb(p)":[86],"for":[87,130,158],"each":[88],"\u2208":[90],"\u2119.":[91],"In":[92],"this":[93],"paper":[94],"show":[96],"locally":[102],"generalized":[103],"radical":[104],"in":[106],"which":[107],"normal":[109],"closures":[110],"cyclic":[113],"subgroups":[114],"rank,":[121],"then":[122],"[G,G]":[123],"[Formula:":[125,133],"see":[126,134],"text]-bounded":[127],"some":[131,142],"function":[132],"text].":[135],"This":[136],"wide":[139],"generalization":[140],"results":[143],"by":[144],"Neumann,":[145],"Smith":[146],"many":[148],"others.":[149],"Moreover":[150],"are":[152],"able":[153],"give":[155],"explicit":[156],"formulas":[157],"involved":[160],"bounds.":[161]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}