{"?xml":{"@version":"1.0"},"edm:RDF":{"@xmlns:dc":"http://purl.org/dc/elements/1.1/","@xmlns:edm":"http://www.europeana.eu/schemas/edm/","@xmlns:wgs84_pos":"http://www.w3.org/2003/01/geo/wgs84_pos","@xmlns:foaf":"http://xmlns.com/foaf/0.1/","@xmlns:rdaGr2":"http://rdvocab.info/ElementsGr2","@xmlns:oai":"http://www.openarchives.org/OAI/2.0/","@xmlns:owl":"http://www.w3.org/2002/07/owl#","@xmlns:rdf":"http://www.w3.org/1999/02/22-rdf-syntax-ns#","@xmlns:ore":"http://www.openarchives.org/ore/terms/","@xmlns:skos":"http://www.w3.org/2004/02/skos/core#","@xmlns:dcterms":"http://purl.org/dc/terms/","edm:WebResource":[{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-57MGJAGK/bd2362a3-be80-4c09-8b18-3203ef815eea/PDF","dcterms:extent":"319 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-57MGJAGK/af509742-3ebf-4e8f-be4b-07d36b025c47/TEXT","dcterms:extent":"28 KB"}],"edm:TimeSpan":{"@rdf:about":"2008-2025","edm:begin":{"@xml:lang":"en","#text":"2008"},"edm:end":{"@xml:lang":"en","#text":"2025"}},"edm:ProvidedCHO":{"@rdf:about":"URN:NBN:SI:doc-57MGJAGK","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2016","dc:creator":"Vavpetič, Aleš","dc:format":[{"@xml:lang":"sl","#text":"številka:1"},{"@xml:lang":"sl","#text":"letnik:10"},{"@xml:lang":"sl","#text":"str. 67-77"}],"dc:identifier":["COBISSID:17731929","ISSN:1855-3966","URN:URN:NBN:SI:doc-57MGJAGK"],"dc:language":"en","dc:publisher":{"@xml:lang":"sl","#text":"Univerza na Primorskem, Fakulteta za matematiko, naravoslovje in informacijske tehnologije"},"dc:subject":[{"@xml:lang":"en","#text":"alternating group"},{"@xml:lang":"sl","#text":"alternirajoča grupa"},{"@xml:lang":"sl","#text":"cikel"},{"@xml:lang":"en","#text":"commutator"},{"@xml:lang":"en","#text":"cycle"},{"@xml:lang":"sl","#text":"komutator"},{"@xml:lang":"sl","#text":"permutacija"},{"@xml:lang":"en","#text":"permutation"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"Commutators of cycles in permutation groups|"},"dc:description":[{"@xml:lang":"sl","#text":"We prove that for ?$n \\ge 5$?, every element of the alternating group ?$A_n$? is a commutator of two cycles of ?$A_n$?. Moreover we prove that for ?$n \\ge 2$?, a ?$(2n + 1)$?-cycle of the permutation group ?$S_{2n + 1}$? is a commutator of a ?$p$?-cycle and a ?$q$?-cycle of ?$S_{2n + 1}$? if and only if the following three conditions are satisfied: (i) ?$n + 1 \\le p, q$?, (ii) ?$2n + 1 \\ge p, q$?, (iii) ?$p + q \\ge 3n + 1$?"},{"@xml:lang":"sl","#text":"Dokažemo, da je za ?$n \\ge 5$? vsak element alternirajoče grupe ?$A_n$? komutator dveh ciklov ?$A_n$?. Dokažemo tudi, da je za ?$n \\ge 2$? vsak ?$(2n + 1)$?-cikel permutacijske grupe ?$S_{2n + 1}$? komutator ?$p$?-cikla in ?$q$?-cikla ?$S_{2n + 1}$?, če in samo če so izpolnjeni naslednji trije pogoji: (i)? $n + 1 \\le p, q$?, (ii) ?$2n + 1 \\ge p, q$?, (iii) ?$p + q \\ge 3n + 1$?"}],"edm:type":"TEXT","dc:type":[{"@xml:lang":"sl","#text":"znanstveno časopisje"},{"@xml:lang":"en","#text":"journals"},{"@rdf:resource":"http://www.wikidata.org/entity/Q361785"}]},"ore:Aggregation":{"@rdf:about":"http://www.dlib.si/?URN=URN:NBN:SI:doc-57MGJAGK","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-57MGJAGK"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-57MGJAGK/bd2362a3-be80-4c09-8b18-3203ef815eea/PDF"},"edm:rights":{"@rdf:resource":"http://creativecommons.org/licenses/by/4.0/"},"edm:provider":"Slovenian National E-content Aggregator","edm:intermediateProvider":{"@xml:lang":"en","#text":"National and University Library of Slovenia"},"edm:dataProvider":{"@xml:lang":"sl","#text":"Univerza na Primorskem, Fakulteta za naravoslovje, matematiko in informacijske tehnologije"},"edm:object":{"@rdf:resource":"http://www.dlib.si/streamdb/URN:NBN:SI:doc-57MGJAGK/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-57MGJAGK"}}}}