{"?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-1NYXBWE5/ff3e79ce-9294-446d-9029-db67e0a78554/PDF","dcterms:extent":"363 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:DOC-1NYXBWE5/3a7fa951-7e74-4b2d-8df4-6cbb1c60a7fe/TEXT","dcterms:extent":"27 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-1NYXBWE5","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2021","dc:creator":["Glasby, Stephen P.","Pierro, Emilio","Praeger, Cheryl E."],"dc:format":[{"@xml:lang":"sl","#text":"številka:2"},{"@xml:lang":"sl","#text":"letnik:21"},{"@xml:lang":"sl","#text":"str. 309-317"}],"dc:identifier":["DOI:10.26493/1855-3974.2049.3db","COBISSID_HOST:112945667","ISSN:1855-3966","URN:URN:NBN:SI:doc-1NYXBWE5"],"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":"generalised hexagon"},{"@xml:lang":"en","#text":"generalised octagon"},{"@xml:lang":"en","#text":"generalised polygon"},{"@xml:lang":"sl","#text":"posplošeni mnogokotnik"},{"@xml:lang":"sl","#text":"posplošeni osemkotnik"},{"@xml:lang":"sl","#text":"posplošeni šestkotnik"},{"@xml:lang":"en","#text":"primitive permutation group"},{"@xml:lang":"sl","#text":"primitivna permutacijska grupa"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"Point-primitive generalised hexagons and octagons and projective linear groups|"},"dc:description":[{"@xml:lang":"sl","#text":"We discuss recent progress on the problem of classifying point-primitive generalised polygons. In the case of generalised hexagons and generalised octagons, this has reduced the problem to primitive actions of almost simple groups of Lie type. To illustrate how the natural geometry of these groups may be used in this study, we show that if ?$\\mathcal{S}$? is a finite thick generalised hexagon or octagon with ?$G \\leqslant \\text{Aut}(\\mathcal{S})$? acting point-primitively and the socle of ?$\\mathcal{G}$? isomorphic to ?$\\mathrm{PSL}_n(q)$? where ?$n\\geqslant 2$?, then the stabiliser of a point acts irreducibly on the natural module. We describe a strategy to prove that such a generalised hexagon or octagon ?$\\mathcal{S}$? does not exist"},{"@xml:lang":"sl","#text":"Predstavimo nedavni preboj v zvezi s problemom klasificiranja točkovno primitivnih posplošenih mnogokotnikov. V primeru posplošenih šestkotnikov in posplošenih osemkotnikov se na podlagi tega rezultata omenjeni problem poenostavi na obravnavo primitivnih delovanj skoraj enostavnih Liejevih grup. Kot primer, kako se da naravno geometrijo teh grup uporabiti pri tej raziskavi, pokažemo, da če je ?$\\mathcal{S}$? končen odebeljen posplošen šestkotnik ali osemkotnik, na katerem grupa ?$G\\leqslant\\text{Aut}(\\mathcal{S})$? deluje točkovno primitivno, njen podstavek pa je izomorfen ?$\\mathrm{PSL}_n(q)$?, kjer je ?$n\\geqslant 2$?, potem stabilizator poljubne točke deluje ireducibilno na naravnem modulu. Opišemo strategijo dokaza, da tak posplošeni šestkotnik oz. osemkotnik ?$\\mathcal{S}$? ne obstaja"}],"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-1NYXBWE5","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:DOC-1NYXBWE5"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:DOC-1NYXBWE5/ff3e79ce-9294-446d-9029-db67e0a78554/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-1NYXBWE5/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:DOC-1NYXBWE5"}}}}