Maximal unramified extensions of quadratic number fields have been well studied. This thesis focuses on maximal unramified extensions of cyclic cubic fields. We use the unconditional discriminant bounds of Moreno to determine cyclic cubic fields having no non-solvable unramified extensions. We also use a theorem of Roquette, developed from the method of Golod-Shafarevich, and some results by Cohen to construct cyclic cubic fields in which the unramified extension is of infinite degree.
College and Department
Physical and Mathematical Sciences; Mathematics
BYU ScholarsArchive Citation
Wong, Ka Lun, "Maximal Unramified Extensions of Cyclic Cubic Fields" (2011). All Theses and Dissertations. 2781.
Maximal unramified extensions, cyclic cubic fields