{"?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-9D93JITH/d58f6757-fd74-47c8-9497-5f970e8e6116/PDF","dcterms:extent":"408 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-9D93JITH/87af04b2-a6d2-4cc2-b05c-9d58031fb03d/TEXT","dcterms:extent":"33 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-9D93JITH","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":["Korchmáros, Gábor","Nagy, Gábor Péter"],"dc:format":[{"@xml:lang":"sl","#text":"številka:1"},{"@xml:lang":"sl","#text":"letnik:20"},{"@xml:lang":"sl","#text":"str. 89-102"}],"dc:identifier":["DOI:10.26493/1855-3974.2154.cda","ISSN:1855-3966","COBISSID_HOST:91616515","URN:URN:NBN:SI:doc-9D93JITH"],"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":"Cayley graph"},{"@xml:lang":"sl","#text":"Cayleyjev graf"},{"@xml:lang":"en","#text":"Frobenius graphical representation"},{"@xml:lang":"en","#text":"Frobenius group"},{"@xml:lang":"sl","#text":"Frobeniusova grafovska predstavitev"},{"@xml:lang":"sl","#text":"Frobeniusova grupa"},{"@xml:lang":"en","#text":"Suzuki 2-group"},{"@xml:lang":"sl","#text":"Suzukijeva 2-grupa"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"Graphical Frobenius representations of non-abelian groups|"},"dc:description":[{"@xml:lang":"sl","#text":"A group ?$G$? has a Frobenius graphical representation (GFR) if there is a simple graph ?$\\Gamma$? whose full automorphism group is isomorphic to ?$G$? acting on the vertices as a Frobenius group. In particular, any group ?$G$? with a GFR is a Frobenius group and ?$\\Gamma$? is a Cayley graph. By very recent results of Spiga, there exists a function ?$f$? such that if ?$G$? is a finite Frobenius group with complement ?$H$? and ?$|G| > f(|H|)$? then ?$G$? admits a GFR. This paper provides an infinite family of graphs that admit GFRs despite not meeting Spiga's bound. In our construction, the group ?$G$? is the Higman group ?$A(f, q_0)$? for an infinite sequence of ?$f$? and ?$q_0$?, having a nonabelian kernel and a complement of odd order"},{"@xml:lang":"sl","#text":"Grupa ?$G$? ima Frobeniusovo grafovsko predstavitev, če obstaja enostaven graf ?$\\Gamma$?, katerega polna grupa avtomorfizmov je izomorfna grupi ?$G$?, ki deluje na vozliščih kot Frobeniusova grupa. Vsaka grupa ?$G$?, ki ima takšno predstavitev, je Frobeniusova grupa in ?$\\Gamma$? je Cayleyjev graf. Po nedavnih rezultatih Spige, obstaja funkcija ?$f$?, za katero velja, da če je ?$G$? končna Frobeniusova grupa s komplementom ?$H$? in je ?$|G| > f(|H|)$?, potem ?$G$? dopušča Frobeniusovo grafovsko predstavitev. V tem predstavimo neskončno družino grafov, ki dopuščajo Frobeniusovo grafovsko predstavitev, čeprav ne ustrezajo Spigovi meji. V naši konstrukciji je grupa ?$G$? Higmanova grupa ?$A(f, q_0)$? za neskončno zaporedje funkcij ?$f$? in ?$q_0$?, ki ima nekomutativno jedro ter komplement lihega reda"}],"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-9D93JITH","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-9D93JITH"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-9D93JITH/d58f6757-fd74-47c8-9497-5f970e8e6116/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-9D93JITH/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-9D93JITH"}}}}