The Structure of the Class Group of Imaginary Quadratic Fields

Let 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.

Name thesis:degree_name

Master of Science

Level thesis:degree_level

masters

Discipline thesis:degree_discipline

Mathematics

Department dc:contributor.department

Mathematics

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

2005

Author dc:creator

• Miller, Nicole Renee

Chair dc:contributor.committeechair

• Parry, Charles J.

Committee members dc:contributor.committeemember

• Haskell, Peter E.
• Brown, Ezra A.

• 7-rank
• 5-rank
• Positive Definite Forms
• Genera
• Class Group
• Binary Quadratic Fields

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Dc Identifier Other

etd-05112005-124308

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/32572