Type of Document	Dissertation
Author	Taylor, Frank Seaton
Author's Email Address	prime@vt.edu
URN	etd-111897-10412
Title	Quintic Abelian Fields
Degree	PhD
Department	Mathematics
Advisory Committee	Advisor Name Title Parry, Charles J. Committee Chair Ball, Joseph A. Committee Member Brown, Ezra A. Committee Member Floyd, William J. Committee Member Johnson, Lee W. Committee Member
Keywords	Abelian Fields Class Number Conductor Fundamental Unit Quintic Fields
Date of Defense	1997-12-17
Availability	unrestricted
Abstract Quintic abelian fields are characterized in terms of their conductor and a certain Galois group. From these, a generating polynomial and its roots and an integral basis are computed. A method for finding the fundamental units, regulators and class numbers is then developed. Tables listing the coefficients of a generating polynomial, the regulator, the class number, and a coefficients of a fundamental unit are given for 1527 quintic abelian fields. Of the seven cases where the class group structure is not immediate from the class number, six have their structure computed.
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