Type of Document 
Dissertation 
Author 
Chalmeta, A. Pablo

URN 
etd10042006220651 
Title 
On the Units and the Structure of the 3Sylow 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 
20060929 
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 3class group.

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