Type of Document	Master's Thesis
Author	Miller, Nicole Renee
Author's Email Address	nimille2@vt.edu
URN	etd-05112005-124308
Title	The Structure of the Class Group of Imaginary Quadratic Fields
Degree	Master of Science
Department	Mathematics
Advisory Committee	Advisor Name Title Parry, Charles J. Committee Chair Brown, Ezra A. Committee Member Haskell, Peter E. Committee Member
Keywords	7-rank 5-rank Positive Definite Forms Genera Class Group Binary Quadratic Fields
Date of Defense	2005-05-11
Availability	unrestricted
Abstract Let $Q(\sqrt{-d})$ be an imaginary quadratic field with discriminant $\Delta$. 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.
Files	Filename       Size       Approximate Download Time (Hours:Minutes:Seconds)     28.8 Modem   56K Modem   ISDN (64 Kb)   ISDN (128 Kb)   Higher-speed Access    Nicole.pdf 236.77 Kb 00:01:05 00:00:33 00:00:29 00:00:14 00:00:01

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