{"?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-KM2BASE7/0DD982F1-E504-4887-B0AB-2DE99CB7D55C/PDF","dcterms:extent":"0 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-KM2BASE7/ce013353-4156-4e56-874f-20c0c6e2658a/PDF","dcterms:extent":"266 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-KM2BASE7/a278f5b2-e486-4e2b-a398-7433c0bfdc34/TEXT","dcterms:extent":"31 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-KM2BASE7","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2011","dc:creator":["Conder, Marston D. E.","Tucker, Thomas W."],"dc:format":[{"@xml:lang":"sl","#text":"številka:1"},{"@xml:lang":"sl","#text":"letnik:4"},{"@xml:lang":"sl","#text":"str. 63-72"}],"dc:identifier":["COBISSID:16262489","ISSN:1855-3966","URN:URN:NBN:SI:doc-KM2BASE7"],"dc:language":"en","dc:publisher":{"@xml:lang":"sl","#text":"Društvo matematikov, fizikov in astronomov Slovenije"},"dc:subject":[{"@xml:lang":"sl","#text":"delovanje grupe"},{"@xml:lang":"en","#text":"distinguishing number"},{"@xml:lang":"sl","#text":"gibanje"},{"@xml:lang":"en","#text":"group action"},{"@xml:lang":"en","#text":"motion"},{"@xml:lang":"sl","#text":"razlikovalno število"},{"@xml:lang":"sl","#text":"stabilizator"},{"@xml:lang":"en","#text":"stabilizer"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"Motion and distinguishing number two|"},"dc:description":{"@xml:lang":"sl","#text":"A group ?$A$? acting faithfully on a finite set ?$X$? is said to have distinguishing number two if there is a proper subset ?$Y$? whose (setwise) stabilizer is trivial. The motion of ?$A$? acting on ?$X$? is defined as the largest integer ?$k$? such that all non-trivial elements of ?$A$? move at least ?$k$? elements of ?$X$?. The Motion Lemma of Russell and Sundaram states that if the motion is at least ?$2 \\log_2 |A|$?, then the action has distinguishing number two. When ?$X$? is a vector space, group, or map, the Motion Lemma and elementary estimates of the motion together show that in all but finitely many cases, the action of Aut?$(X)$? on ?$X$? has distinguishing number two. A new lower bound for the motion of any transitive action gives similar results for transitive actions with restricted point-stabilizers. As an instance of what can happen with intransitive actions, it is shown that if ?$X$? is a set of points on a closed surface of genus ?$g$?, and ?$|X|$? is sufficiently large with respect to ?$g$?, then any action on ?$X$? by a finite group of surface homeomorphisms has distinguishing number two"},"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-KM2BASE7","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-KM2BASE7"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-KM2BASE7/0DD982F1-E504-4887-B0AB-2DE99CB7D55C/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-KM2BASE7/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-KM2BASE7"}}}}