On the Units and the Structure of the 3-Sylow Subgroups of the Ideal Class Groups of Pure Bicubic Fields and their Normal Closures

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dc.contributor.authorChalmeta, A. Pabloen
dc.contributor.committeechairParry, Charles J.en
dc.contributor.committeememberRenardy, Michael J.en
dc.contributor.committeememberGreen, Edward L.en
dc.contributor.committeememberLinnell, Peter A.en
dc.contributor.committeememberBrown, Ezra A.en
dc.contributor.departmentMathematicsen
dc.date.accessioned2014-03-14T20:17:05Zen
dc.date.adate2006-11-20en
dc.date.available2014-03-14T20:17:05Zen
dc.date.issued2006-09-29en
dc.date.rdate2009-11-20en
dc.date.sdate2006-10-04en
dc.description.abstractIf we adjoin the cube root of a cube free rational integer <i>m</i> to the rational numbers we construct a cubic field. If we adjoin the cube roots of distinct cube free rational integers <i>m</i> and <i>n</i> to the rational numbers we construct a bicubic field. The number theoretic invariants for the cubic fields and their normal closures are well known. Some work has been done on the units, classnumbers and other invariants of the bicubic fields and their normal closures by Parry but no method is available for calculating those invariants. This dissertation provides an algorithm for calculating the number theoretic invariants of the bicubic fields and their normal closure. Among these invariants are the discriminant, an integral basis, a set of fundamental units, the class number and the rank of the 3-class group.en
dc.description.degreePh. D.en
dc.identifier.otheretd-10042006-220651en
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-10042006-220651/en
dc.identifier.urihttp://hdl.handle.net/10919/29191en
dc.publisherVirginia Techen
dc.relation.haspartchalmeta.pdfen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectBicubic Fieldsen
dc.subjectInvariantsen
dc.subjectIdeal Class Groupen
dc.subjectNormal Closureen
dc.subjectClass Numberen
dc.titleOn the Units and the Structure of the 3-Sylow Subgroups of the Ideal Class Groups of Pure Bicubic Fields and their Normal Closuresen
dc.typeDissertationen
thesis.degree.disciplineMathematicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.leveldoctoralen
thesis.degree.namePh. D.en

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