{"?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-UWBLEQLZ/dfdaeda6-c2f1-4396-ab2a-5f74974b7eb8/PDF","dcterms:extent":"436 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-UWBLEQLZ/141a4b30-c028-427e-acc0-7d94cc6d89e0/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-UWBLEQLZ","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2017","dc:creator":["Bonetta-Martin, Kyle","McCourt, Thomas A."],"dc:format":[{"@xml:lang":"sl","#text":"številka:1"},{"@xml:lang":"sl","#text":"letnik:13"},{"@xml:lang":"sl","#text":"str. 167-185"}],"dc:identifier":["COBISSID:18199641","ISSN:1855-3966","URN:URN:NBN:SI:doc-UWBLEQLZ"],"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":"abelska sipinska grupa"},{"@xml:lang":"sl","#text":"kanonična grupa"},{"@xml:lang":"sl","#text":"sferični par latinskih kvadratov"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"On which groups can arise as the canonical group of a spherical latin bitrade|"},"dc:description":[{"@xml:lang":"sl","#text":"We address a question of Cavenagh and Wanless asking: which finite abelian groups arise as the canonical group of a spherical latin bitrade? We prove the existence of an infinite family of finite abelian groups that do not arise as canonical groups of spherical latin bitrades. Using a connection between abelian sandpile groups of digraphs underlying directed Eulerian spherical embeddings, we go on to provide several, general, families of finite abelian groups that do arise as canonical groups. These families include: (1) any abelian group in which each component of the Smith Normal Form has composite order; (2) any abelian group with Smith Normal Form ?$\\mathbb{Z}_{p}^{n} (\\oplus_{i = 1}^{k}\\mathbb{Z}_{pa_{i}})$?, where ?$1 \\leq k$?, ?$2 \\leq a_{1},a_{2},\\ldots,a_{k},p$? and ?$n \\leq 1 + 2\\sum_{i = 1}^{k}(a_{i} - 1)$?; and (3) with two exceptions and two potential exceptions any abelian group of rank two"},{"@xml:lang":"sl","#text":"Obravnavamo vprašanje, ki sta ga zastavila Cavenagh in Wanless: katere končne abelske grupe lahko dobimo kot kanonične grupe kakšnega sferičnega para latinskih kvadratov? Dokažemo obstoj neskončne družine abelskih grup, ki jih ne dobimo kot kanonične družine sferičnih parov latinskih kvadratov. Z uporabo zveze med abelskimi sipinskimi grupami digrafov, osnovanih na usmerjenih eulerskih sferičnih vložitvah, najdemo več splošnih družin končnih abelskih grup, ki jih dobimo kot kanonične grupe. Te družine vključujejo: (1) vsako abelsko grupo v kateri ima vsaka komponenta Smithove normalne forme sestavljen red; (2) vsako abelsko grupo s Smithovo normalno formo ?$\\mathbb{Z}_{p}^{n} (\\oplus_{i = 1}^{k}\\mathbb{Z}_{pa_{i}})$?, kjer je ?$1 \\leq k$?, ?$2 \\leq a_{1},a_{2},\\ldots,a_{k},p$? in ?$n \\leq 1 + 2\\sum_{i = 1}^{k}(a_{i} - 1)$?; in (3) z dvema izjemama in dvema morebitnima izjemama vsako abelsko grupo ranga dve"}],"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-UWBLEQLZ","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-UWBLEQLZ"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-UWBLEQLZ/dfdaeda6-c2f1-4396-ab2a-5f74974b7eb8/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-UWBLEQLZ/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-UWBLEQLZ"}}}}