In this thesis, we define a certain group of order 160, which we call a hyperpentagonal group, and we prove that every totally real D5-extension of the rationals ramified at only one prime is contained in a hyperpentagonal extension of the rationals. This generalizes a result of Doud and Childers (originally conjectured by Wong) that every totally real S3 extension of the rationals ramified at only one prime is contained in an S4 extension.
College and Department
Physical and Mathematical Sciences; Mathematics
BYU ScholarsArchive Citation
Rodriguez, Pablo Miguel, "Pentagonal Extensions of the Rationals Ramified at a Single Prime" (2021). Theses and Dissertations. 9342.
algebraic number theory, number theory, algebra