Title page for ETD etd-10042006-220651


Type of Document Dissertation
Author Chalmeta, A. Pablo
URN etd-10042006-220651
Title On the Units and the Structure of the 3-Sylow Subgroups of the Ideal Class Groups of Pure Bicubic Fields and their Normal Closures
Degree PhD
Department Mathematics
Advisory Committee
Advisor Name Title
Parry, Charles J. Committee Chair
Brown, Ezra A. Committee Member
Green, Edward L. Committee Member
Linnell, Peter A. Committee Member
Renardy, Michael J. Committee Member
Keywords
  • Bicubic Fields
  • Invariants
  • Ideal Class Group
  • Normal Closure
  • Class Number
Date of Defense 2006-09-29
Availability unrestricted
Abstract
If we adjoin the cube root of a cube free rational integer m to the rational numbers we construct a cubic field. If we adjoin the cube roots of distinct cube free rational integers m and n 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.
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