{"?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-UJWV8CKX/d83a449a-5513-4683-a2ed-9d2d5ed36b67/PDF","dcterms:extent":"378 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-UJWV8CKX/0fca59da-6b86-47cc-99d4-894125822e9f/TEXT","dcterms:extent":"37 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-UJWV8CKX","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2022","dc:creator":["May, Coy L.","Zimmerman, Jay"],"dc:format":[{"@xml:lang":"sl","#text":"številka:1"},{"@xml:lang":"sl","#text":"letnik:22"},{"@xml:lang":"sl","#text":"P1.09 (13 str.)"}],"dc:identifier":["DOI:10.26493/1855-3974.2257.6de","COBISSID_HOST:115590659","ISSN:1855-3966","URN:URN:NBN:SI:doc-UJWV8CKX"],"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":"delovanje grupe"},{"@xml:lang":"en","#text":"genus"},{"@xml:lang":"en","#text":"group action"},{"@xml:lang":"sl","#text":"močni simetrični rod"},{"@xml:lang":"en","#text":"NEC group"},{"@xml:lang":"sl","#text":"NEC grupa"},{"@xml:lang":"en","#text":"Riemann surface"},{"@xml:lang":"sl","#text":"Riemannova ploskev"},{"@xml:lang":"sl","#text":"rod"},{"@xml:lang":"en","#text":"strong symmetric genus"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"Maximal order group actions on Riemann surfaces|"},"dc:description":[{"@xml:lang":"sl","#text":"A natural problem is to determine, for each value of the integer ?$g \\ge 2$?, the largest order of a group that acts on a Riemann surface of genus ?$g$?. Let ?$N(g)$? (respectively ?$M(g)$?) be the largest order of a group of automorphisms of a Riemann surface of genus ?$g \\ge 2$? preserving the orientation (respectively possibly reversing the orientation) of the surface. The basic inequalities comparing ?$N(g)$? and ?$M(g)$? are ?$N(g) \\le M(g) \\le 2N(g)$?. There are well-known families of extended Hurwitz groups that provide an infinite number of integers ?$g$? satisfying ?$M(g) = 2N(g)$?. It is also easy to see that there are solvable groups which provide an infinite number of such examples. We prove that, perhaps surprisingly, there are an infinite number of integers ?$g$? such that ?$N(g) = M(g)$?. Specifically, if ?$p$? is a prime satisfying ?$p \\equiv 1 (mod 6)$? and ?$g = 3p + 1$? or ?$g = 2p+1$?, there is a group of order ?$24(g - 1)$? that acts on a surface of genus ?$g$? preserving the orientation of the surface. For all such values of $g$ larger than a fixed constant, there are no groups with order larger than ?$24(g - 1)$? that act on a surface of genus ?$g$?"},{"@xml:lang":"sl","#text":"Kako določiti, za vsako vrednost celega števila ?$g \\ge 2$?, največji red grupe, ki deluje na Riemannovi ploskvi rodu ?$g$?, je zelo naraven problem. Naj bo ?$N(g)$? največji red grupe avtomorfizmov Riemannove ploskve rodu ?$g \\ge 2$?, ki ohranjajo orientacijo ploskve, ?$M(g)$? pa tistih, ki orientacijo morda obrnejo. Osnovne neenakosti, ki primerjajo ?$N(g)$? in ?$M(g)$?, so: ?$N(g) \\le M(g) \\le 2N(g)$?. Dobro znane so družine razširjenih Hurwitzevih grup, iz katerih dobimo neskončno mnogo celih števil ?$g$?, ki zadoščajo enakosti ?$M(g) = 2N(g)$?. Lahko je tudi videti, da obstajajo rešljive grupe, iz katerih dobimo neskončno mnogo takih primerov. Dokažemo, kar morda preseneča, da obstaja neskončno mnogo celih števil ?$g$?, za katera je ?$N(g) = M(g)$?. V primeru, da je ?$p$? praštevilo, ki zadošča ?$p \\equiv 1 (mod 6)$? in ?$g = 3p + 1$? ali ?$g = 2p+1$?, obstaja grupa reda ?$24(g - 1)$?, ki deluje na neki ploskvi rodu ?$g$?, pri čemer ohranja njeno orientacijo. Za vse vrednosti ?$g$?, ki so večje od neke fiksne konstante, ne obstajajo grupe z redom večjim od ?$24(g - 1)$?, ki bi delovale na ploskvi rodu ?$g$?"}],"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-UJWV8CKX","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-UJWV8CKX"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-UJWV8CKX/d83a449a-5513-4683-a2ed-9d2d5ed36b67/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-UJWV8CKX/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-UJWV8CKX"}}}}