The Structure of the Class Group of Imaginary Quadratic Fields

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dc.contributor.authorMiller, Nicole Reneeen
dc.contributor.committeechairParry, Charles J.en
dc.contributor.committeememberHaskell, Peter E.en
dc.contributor.committeememberBrown, Ezra A.en
dc.contributor.departmentMathematicsen
dc.date.accessioned2014-03-14T20:36:17Zen
dc.date.adate2005-05-24en
dc.date.available2014-03-14T20:36:17Zen
dc.date.issued2005-05-11en
dc.date.rdate2008-05-24en
dc.date.sdate2005-05-11en
dc.description.abstractLet Q(√(-d)) be an imaginary quadratic field with discriminant Δ. We use the isomorphism between the ideal class groups of the field and the equivalence classes of binary quadratic forms to find the structure of the class group. We determine the structure by combining two of Shanks' algorithms [7, 8]. We utilize this method to find fields with cyclic factors that have order a large power of 2, or fields with class groups of high 5-ranks or high 7-ranks.en
dc.description.degreeMaster of Scienceen
dc.identifier.otheretd-05112005-124308en
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-05112005-124308/en
dc.identifier.urihttp://hdl.handle.net/10919/32572en
dc.publisherVirginia Techen
dc.relation.haspartNicole.pdfen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subject7-ranken
dc.subject5-ranken
dc.subjectPositive Definite Formsen
dc.subjectGeneraen
dc.subjectClass Groupen
dc.subjectBinary Quadratic Fieldsen
dc.titleThe Structure of the Class Group of Imaginary Quadratic Fieldsen
dc.typeThesisen
thesis.degree.disciplineMathematicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.levelmastersen
thesis.degree.nameMaster of Scienceen

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