AuthorMarshall, David Clark
AdvisorMcCallum, William G.
MetadataShow full item record
PublisherThe University of Arizona.
RightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
AbstractWe consider the structure of a certain infinite Galois group over Q(ζp) the cyclotomic field of p-th roots of unity. Namely, we consider the Galois group of the maximal p-ramified pro- p-extension. Very little is known about this group. It has a free pro-p presentation in terms of g generators and s relations where g and s may be explicitly computed in terms of the p-rank of the class group of Q(ζp). The structure of the relations in the Galois group are shown to be very closely related to the relations in a certain Iwasawa module. The main result of this dissertation shows this Iwasawa module to be torsion free for a large class of cyclotomic fields. The result is equivalent to verifying Greenberg's pseudo-null conjecture for the given class of fields. As one consequence, we provide a large class of examples of cyclotomic fields which do not admit free pro-p-extensions of maximal rank.
Degree ProgramGraduate College