| fullrecord |
[{"key": "dc.contributor.advisor", "value": "Parkkonen, Jouni", "language": null, "element": "contributor", "qualifier": "advisor", "schema": "dc"}, {"key": "dc.contributor.author", "value": "Aittoniemi, Elina", "language": null, "element": "contributor", "qualifier": "author", "schema": "dc"}, {"key": "dc.date.accessioned", "value": "2024-05-03T05:08:28Z", "language": null, "element": "date", "qualifier": "accessioned", "schema": "dc"}, {"key": "dc.date.available", "value": "2024-05-03T05:08:28Z", "language": null, "element": "date", "qualifier": "available", "schema": "dc"}, {"key": "dc.date.issued", "value": "2024", "language": null, "element": "date", "qualifier": "issued", "schema": "dc"}, {"key": "dc.identifier.uri", "value": "https://jyx.jyu.fi/handle/123456789/94648", "language": null, "element": "identifier", "qualifier": "uri", "schema": "dc"}, {"key": "dc.description.abstract", "value": "T\u00e4m\u00e4n sivututkielman tarkoituksena on luokitella \u00e4\u00e4rellisi\u00e4 ryhmi\u00e4 isomorfialla kertalukuun 21 saakka. Luokittelussa hy\u00f6dynnet\u00e4\u00e4n muun muassa Lagrangen ja Cauchyn lauseita sek\u00e4 my\u00f6hemmin Sylowin lauseita. N\u00e4m\u00e4 antavat pohjaa ryhmien rakenteiden hahmottamiseen.\nEnsimm\u00e4iseksi ty\u00f6ss\u00e4 k\u00e4yd\u00e4\u00e4n l\u00e4pi ryhm\u00e4teorialle ominaisia m\u00e4\u00e4ritelmi\u00e4 ja\nk\u00e4sitteit\u00e4 sek\u00e4 Lagrangen lause ja isomorfia. T\u00e4m\u00e4n j\u00e4lkeen esitell\u00e4\u00e4n ryhm\u00e4perheet, joiden yhteydess\u00e4 k\u00e4yd\u00e4\u00e4n l\u00e4pi esimerkiksi kertaluvultaan alkuluvullisen ryhm\u00e4n luokittelu sek\u00e4 erikoistapauksen 8 k\u00e4sittely.\nT\u00e4m\u00e4n j\u00e4lkeen perehdyt\u00e4\u00e4n ryhm\u00e4n toimintaan, rataan, stabiloijaan sek\u00e4\nrata-stabiloijalauseeseen konjugaation n\u00e4k\u00f6kulmasta. K\u00e4yd\u00e4\u00e4n l\u00e4pi luokkayht\u00e4l\u00f6, keskus ja keskitt\u00e4j\u00e4 sek\u00e4 Cauchyn lause, joiden yhteydess\u00e4 tarkastellaan kertalukujen tapausten p^2 ja 2p, miss\u00e4 p on alkuluku, todistukset.\nViimeiseksi esitell\u00e4\u00e4n p-aliryhm\u00e4t sek\u00e4 erityisesti Sylowin lauseet ja niiden\ntodistukset. N\u00e4m\u00e4 antavat pohjaa kertalukujen erikoistapauksen 12 sek\u00e4 yleisen tapauksen pq, miss\u00e4 p ja q ovat eri alkulukuja, tarkempaan perehtymiseen. N\u00e4iden j\u00e4lkeen m\u00e4\u00e4ritell\u00e4\u00e4n puolisuora tulo sek\u00e4 esitell\u00e4\u00e4n pintapuolisesti kertaluvun erikoistapaukset 16, 18 ja 20 viitaten niit\u00e4 syvemmin k\u00e4sitteleviin teoksiin. Kertaluvun tapaukset 1 \u2212 21 on koottu ty\u00f6n loppuun\nliitteeksi.", "language": "fi", "element": "description", "qualifier": "abstract", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Submitted by Paivi Vuorio (paelvuor@jyu.fi) on 2024-05-03T05:08:28Z\nNo. of bitstreams: 0", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Made available in DSpace on 2024-05-03T05:08:28Z (GMT). No. of bitstreams: 0\n Previous issue date: 2024", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.format.extent", "value": "40", "language": "", "element": "format", "qualifier": "extent", "schema": "dc"}, {"key": "dc.format.mimetype", "value": "application/pdf", "language": null, "element": "format", "qualifier": "mimetype", "schema": "dc"}, {"key": "dc.language.iso", "value": "fin", "language": null, "element": "language", "qualifier": "iso", "schema": "dc"}, {"key": "dc.rights", "value": "In Copyright", "language": "en", "element": "rights", "qualifier": null, "schema": "dc"}, {"key": "dc.subject.other", "value": "Sylowin lauseet", "language": "", "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "\u00e4\u00e4rellisten ryhmien luokittelu", "language": "", "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.title", "value": "\u00c4\u00e4rellisten ryhmien luokittelusta", "language": null, "element": "title", "qualifier": null, "schema": "dc"}, {"key": "dc.type", "value": "master thesis", "language": null, "element": "type", "qualifier": null, "schema": "dc"}, {"key": "dc.identifier.urn", "value": "URN:NBN:fi:jyu-202405033274", "language": null, "element": "identifier", "qualifier": "urn", "schema": "dc"}, {"key": "dc.type.ontasot", "value": "Master\u2019s thesis", "language": "en", "element": "type", "qualifier": "ontasot", "schema": "dc"}, {"key": "dc.type.ontasot", "value": "Pro gradu -tutkielma", "language": "fi", "element": "type", "qualifier": "ontasot", "schema": "dc"}, {"key": "dc.contributor.faculty", "value": "Faculty of Sciences", "language": "en", "element": "contributor", "qualifier": "faculty", "schema": "dc"}, {"key": "dc.contributor.faculty", "value": "Matemaattis-luonnontieteellinen tiedekunta", "language": "fi", "element": "contributor", "qualifier": "faculty", "schema": "dc"}, {"key": "dc.contributor.department", "value": "Department of Mathematics and Statistics", "language": "en", "element": "contributor", "qualifier": "department", "schema": "dc"}, {"key": "dc.contributor.department", "value": "Matematiikan ja tilastotieteen laitos", "language": "fi", "element": "contributor", "qualifier": "department", "schema": "dc"}, {"key": "dc.contributor.organization", "value": "University of Jyv\u00e4skyl\u00e4", "language": "en", "element": "contributor", "qualifier": "organization", "schema": "dc"}, {"key": "dc.contributor.organization", "value": "Jyv\u00e4skyl\u00e4n yliopisto", "language": "fi", "element": "contributor", "qualifier": "organization", "schema": "dc"}, {"key": "dc.subject.discipline", "value": "Mathematics", "language": "en", "element": "subject", "qualifier": "discipline", "schema": "dc"}, {"key": "dc.subject.discipline", "value": "Matematiikka", "language": "fi", "element": "subject", "qualifier": "discipline", "schema": "dc"}, {"key": "yvv.contractresearch.funding", "value": "0", "language": "", "element": "contractresearch", "qualifier": "funding", "schema": "yvv"}, {"key": "dc.type.coar", "value": "http://purl.org/coar/resource_type/c_bdcc", "language": null, "element": "type", "qualifier": "coar", "schema": "dc"}, {"key": "dc.rights.copyright", "value": "\u00a9 The Author(s)", "language": null, "element": "rights", "qualifier": "copyright", "schema": "dc"}, {"key": "dc.rights.accesslevel", "value": "openAccess", "language": null, "element": "rights", "qualifier": "accesslevel", "schema": "dc"}, {"key": "dc.type.publication", "value": "masterThesis", "language": null, "element": "type", "qualifier": "publication", "schema": "dc"}, {"key": "dc.subject.oppiainekoodi", "value": "4041", "language": null, "element": "subject", "qualifier": "oppiainekoodi", "schema": "dc"}, {"key": "dc.subject.yso", "value": "matematiikka", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.subject.yso", "value": "ryhm\u00e4teoria", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.subject.yso", "value": "algebra", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.format.content", "value": "fulltext", "language": null, "element": "format", "qualifier": "content", "schema": "dc"}, {"key": "dc.rights.url", "value": "https://rightsstatements.org/page/InC/1.0/", "language": null, "element": "rights", "qualifier": "url", "schema": "dc"}]
|