Pentagonal Extensions of the Rationals Ramified at a Single Prime

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 (...

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Main Author:	Rodriguez, Pablo Miguel
Format:	Others
Published:	BYU ScholarsArchive 2021
Subjects:	algebraic number theory number theory algebra Physical Sciences and Mathematics
Online Access:	https://scholarsarchive.byu.edu/etd/9342 https://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=10351&context=etd

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spelling	ndltd-BGMYU2-oai-scholarsarchive.byu.edu-etd-103512021-12-23T05:00:54Z Pentagonal Extensions of the Rationals Ramified at a Single Prime Rodriguez, Pablo Miguel 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. 2021-12-17T08:00:00Z text application/pdf https://scholarsarchive.byu.edu/etd/9342 https://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=10351&context=etd https://lib.byu.edu/about/copyright/ Theses and Dissertations BYU ScholarsArchive algebraic number theory number theory algebra Physical Sciences and Mathematics
collection	NDLTD
format	Others
sources	NDLTD
topic	algebraic number theory number theory algebra Physical Sciences and Mathematics
spellingShingle	algebraic number theory number theory algebra Physical Sciences and Mathematics Rodriguez, Pablo Miguel Pentagonal Extensions of the Rationals Ramified at a Single Prime
description	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.
author	Rodriguez, Pablo Miguel
author_facet	Rodriguez, Pablo Miguel
author_sort	Rodriguez, Pablo Miguel
title	Pentagonal Extensions of the Rationals Ramified at a Single Prime
title_short	Pentagonal Extensions of the Rationals Ramified at a Single Prime
title_full	Pentagonal Extensions of the Rationals Ramified at a Single Prime
title_fullStr	Pentagonal Extensions of the Rationals Ramified at a Single Prime
title_full_unstemmed	Pentagonal Extensions of the Rationals Ramified at a Single Prime
title_sort	pentagonal extensions of the rationals ramified at a single prime
publisher	BYU ScholarsArchive
publishDate	2021
url	https://scholarsarchive.byu.edu/etd/9342 https://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=10351&context=etd
work_keys_str_mv	AT rodriguezpablomiguel pentagonalextensionsoftherationalsramifiedatasingleprime
_version_	1723965557475115008

Pentagonal Extensions of the Rationals Ramified at a Single Prime

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