Taylor, Frank Seaton2014-03-142014-03-141997-12-17etd-111897-10412http://hdl.handle.net/10919/29662Quintic 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.In CopyrightAbelian FieldsClass NumberConductorFundamental UnitQuintic FieldsDissertationhttp://scholar.lib.vt.edu/theses/available/etd-111897-10412/