Abstract/Details

On the index of cyclotomic units


2007 2007

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Abstract (summary)

This thesis is concerned with the unit group and class number of real abelian fields. We study subgroups of the unit group of such fields consisting of cyclotomic units and having index a multiple of the class number. We base our investigation on the work of Greither and Kučcera which provides a minimal generating set for such a subgroup. We refine this minimal generating set so as to obtain subgroup of the unit group whose index is a much smaller multiple of the class number. We outline a strategy for obtaining such refinements in general, and implement it in detail for conductors having two or three prime divisors. In the case of the conductor being divisible by two primes, our cyclotomic units generate a subgroup of index at most twice the class number. In the case of three primes, the index is a somewhat larger multiple of the class number whose exact shape depends on the ramification data.

Indexing (details)


Subject
Mathematics
Classification
0405: Mathematics
Identifier / keyword
Pure sciences, Abelian fields, Class numbers, Cyclotomic units
Title
On the index of cyclotomic units
Author
Greene, Mairead K.
Number of pages
235
Publication year
2007
Degree date
2007
School code
0118
Source
DAI-B 68/07, Dissertation Abstracts International
Place of publication
Ann Arbor
Country of publication
United States
ISBN
9780549175490
Advisor
Hajir, Farshid
University/institution
University of Massachusetts Amherst
Department
Mathematics
University location
United States -- Massachusetts
Degree
Ph.D.
Source type
Dissertations & Theses
Language
English
Document type
Dissertation/Thesis
Dissertation/thesis number
3275791
ProQuest document ID
304838235
Copyright
Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works.
Document URL
http://search.proquest.com/docview/304838235
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