{"?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-8RP9W0T1/61270084-373a-4187-be91-6d0962b66722/PDF","dcterms:extent":"469 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-8RP9W0T1/91ac0a7b-b6e7-4e79-9cb4-4f76d32bf3a6/TEXT","dcterms:extent":"73 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-8RP9W0T1","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2018","dc:creator":["Kalliongis, John","Ryo, Ohashi"],"dc:format":[{"@xml:lang":"sl","#text":"letnik:15"},{"@xml:lang":"sl","#text":"številka:2"},{"@xml:lang":"sl","#text":"str. 297-321"}],"dc:identifier":["COBISSID:18541657","ISSN:1855-3966","URN:URN:NBN:SI:doc-8RP9W0T1"],"dc:language":"en","dc:publisher":{"@xml:lang":"sl","#text":"Univerza na Primorskem, Fakulteta za matematiko, naravoslovje in informacijske tehnologije"},"dc:subject":[{"@xml:lang":"sl","#text":"akiralna simetrija"},{"@xml:lang":"sl","#text":"ekvivalenca delovanj"},{"@xml:lang":"sl","#text":"izometrija"},{"@xml:lang":"sl","#text":"kiralna simetrija"},{"@xml:lang":"sl","#text":"končno delovanje grup"},{"@xml:lang":"sl","#text":"orbifold"},{"@xml:lang":"sl","#text":"simetrija"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"Finite actions on the 2-sphere, the projective plane and I-bundles over the projective plane|"},"dc:description":{"@xml:lang":"sl","#text":"V članku obravnavamo končne grupe, ki delujejo na 2-sferi ?$\\mathbb{S}^2$? in projektivni ravnini ?$\\mathbb{P}^2$?, in pokažemo, kako vizualizirati ta delovanja, ki so eksplicitno definirana. Dobimo njihove kvocientne tipe z razlikovanjem fundamentalne domene za vsako delovanje in identificiranjem njenega roba. Če ?$G$? deluje na ?$\\mathbb{P}^2$?, potem je ?$G$? izomorfna eni od naslednjih grup: ?$\\mathbb{S}_4$?, ?$\\mathbb{A}_5$?, ?$\\mathbb{A}_4$?, ?$\\mathbb{Z}_m$? ali Dih( ?$\\mathbb{Z}_m$?). Za vsako grupo obstaja samo en ekvivalenčni razred (za konjugiranje) in pri delovanju ?$G$? je zanka, ki obrne orientacijo, invariantna, če in samo če je ?$G$? izomorfna bodisi ?$\\mathbb{Z}_m$? bodisi Dih( ?$\\mathbb{Z}_m$?). Z uporabo teh preliminarnih rezultatov klasificiramo in enumeriramo, do ekvivalence natančno, končne grupe, ki delujejo na ?$\\mathbb{P} \\times I$? in zasukanem I-svežnju nad ?$\\mathbb{P}^2$? . Na primer, če je ?$m > 2$? sodo celo število in je ?$m/2$? lih, potem obstajajo na zasukanem I-svežnju nad ?$\\mathbb{P}^2$? trije ekvivalenčni razredi Dih( ?$\\mathbb{Z}_m$?)-delovanj, ki obrnejo orientacijo. Če pa je ?$m/2$? sod, potem sta takšna ekvivalenčna razreda le dva"},"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-8RP9W0T1","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-8RP9W0T1"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-8RP9W0T1/61270084-373a-4187-be91-6d0962b66722/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-8RP9W0T1/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-8RP9W0T1"}}}}