{"?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-BZ20ZC6A/23baac65-f1e5-47f0-a57c-822c639d43f6/PDF","dcterms:extent":"336 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-BZ20ZC6A/9119018a-c7ba-4774-a4c4-105712517eb3/TEXT","dcterms:extent":"40 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-BZ20ZC6A","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2019","dc:creator":["Grech, Mariusz","Imrich, Wilfried","Krystek, Anna Dorota","Wojakowski, Łukasz Jan"],"dc:format":[{"@xml:lang":"sl","#text":"številka:1"},{"@xml:lang":"sl","#text":"letnik:17"},{"@xml:lang":"sl","#text":"str. 89-101"}],"dc:identifier":["ISSN:1855-3966","COBISSID_HOST:18913113","URN:URN:NBN:SI:doc-BZ20ZC6A"],"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":"automorphism group"},{"@xml:lang":"sl","#text":"digraf"},{"@xml:lang":"en","#text":"digraph"},{"@xml:lang":"en","#text":"direct product"},{"@xml:lang":"sl","#text":"direktni produkt"},{"@xml:lang":"sl","#text":"grupa avtomorfizmov"},{"@xml:lang":"sl","#text":"permutacijska grupa"},{"@xml:lang":"en","#text":"permutation group"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"Direct product of automorphism groups of digraphs|"},"dc:description":[{"@xml:lang":"sl","#text":"We study the direct product of automorphism groups of digraphs, where automorphism groups are considered as permutation groups acting on the sets of vertices. By a direct product of permutation groups ?$(A, V ) \\times (B, W)$? we mean the group ?$(A \\times B, V \\times W)$? acting on the Cartesian product of the respective sets of vertices. We show that, except for the infinite family of permutation groups ?$S_n \\times S_n$?, ?$n \\ge 2$?, and four other permutation groups, namely ?$D_4 \\times S_2$?, ?$D_4 \\times D_4$?, ?$S_4 \\times S_2 \\times S_2$?, and ?$C_3 \\times C_3$?, the direct product of automorphism groups of two digraphs is itself the automorphism group of a digraph. In the course of the proof, for each set of conditions on the groups ?$A$? and ?$B$? that we consider, we indicate or build a specific digraph product that, when applied to the digraphs representing ?$A$? and ?$B$?, yields a digraph whose automorphism group is the direct product of ?$A$? and ?$B$?"},{"@xml:lang":"sl","#text":"Študiramo direktni produkt grup avtomorfizmov digrafov, pri čemer grupe avtomorfizmov obravnavamo kot permutacijske grupe, ki delujejo na množicah vozlišč. Direktni produkt permutacijskih grup ?$(A, V ) \\times (B, W)$? je grupa ?$(A \\times B, V \\times W)$?, ki deluje na kartezičnem produktu ustreznih množic vozlišč. Pokažemo, da je direktni produkt grup avtomorfizmov dveh digrafov spet grupa avtomorfizmov digrafa razen v primeru neskončne družine permutacijskih grup ?$S_n \\times S_n$?, ?$n \\ge 2$?, ter še štirih drugih permutacijskih grup in sicer ?$D_4 \\times S_2$?, ?$D_4 \\times D_4$?, ?$S_4 \\times S_2 \\times S_2$? in ?$C_3 \\times C_3$?. To dokažemo tako, da za vsako obravnavano množico pogojev na grupah ?$A$? in ?$B$? navedemo ali zgradimo specificen produkt digrafov. Če ta produkt uporabimo na digrafih, ki pripadata grupama ?$A$? in ?$B$?, dobimo digraf, katerega grupa avtomorfizmov je direktni produkt grup ?$A$? in ?$B$?"}],"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-BZ20ZC6A","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-BZ20ZC6A"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-BZ20ZC6A/23baac65-f1e5-47f0-a57c-822c639d43f6/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-BZ20ZC6A/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-BZ20ZC6A"}}}}