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UBC Theses and Dissertations
Units in integral cyclic group rings for order LRPS Ferguson, Ronald Aubrey
Abstract
For a finite abelian group A, the group of units in the integral group ring ZA may be written as the direct product of its torsion units ±A with a free group U2A . Of finite index in U2A is the group ΩA, the elements of U2 which are mapped to cyclotomic units by each character of A. The order of U2A/ΩA depends on class numbers [formula] in real cyclotomic rings [formula]. Of finite index in ΩA is the group of constructible units YA, for which a multiplicative basis may be explicitly written. The order of ΩA/YA is the circular index c(A). In many cases, for example where A is a p-group with p a regular prime, this index is trivial. This thesis develops an inductive theory for determining c(Cn) where Cn is a cyclic group of order n = lrps, with I and p distinct primes, and also for giving some description of the group ΩCnjYCn. This is a continuation of the work of Hoechsmann for the case n = Ip. It turns out that the methods required for n = lrps are, in general, very different from the ones used for r = s = 1.
Item Metadata
Title |
Units in integral cyclic group rings for order LRPS
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Creator | |
Publisher |
University of British Columbia
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Date Issued |
1997
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Description |
For a finite abelian group A, the group of units in the integral group ring ZA may be written
as the direct product of its torsion units ±A with a free group U2A . Of finite index in U2A is
the group ΩA, the elements of U2 which are mapped to cyclotomic units by each character of
A. The order of U2A/ΩA depends on class numbers [formula] in real cyclotomic rings [formula].
Of finite index in ΩA is the group of constructible units YA, for which a multiplicative basis
may be explicitly written. The order of ΩA/YA is the circular index c(A). In many cases,
for example where A is a p-group with p a regular prime, this index is trivial.
This thesis develops an inductive theory for determining c(Cn) where Cn is a cyclic group
of order n = lrps, with I and p distinct primes, and also for giving some description of the
group ΩCnjYCn. This is a continuation of the work of Hoechsmann for the case n = Ip. It
turns out that the methods required for n = lrps are, in general, very different from the ones
used for r = s = 1.
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Extent |
4012599 bytes
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Genre | |
Type | |
File Format |
application/pdf
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Language |
eng
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Date Available |
2009-04-03
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Provider |
Vancouver : University of British Columbia Library
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Rights |
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.
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DOI |
10.14288/1.0079979
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URI | |
Degree | |
Program | |
Affiliation | |
Degree Grantor |
University of British Columbia
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Graduation Date |
1997-11
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Campus | |
Scholarly Level |
Graduate
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Aggregated Source Repository |
DSpace
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Item Media
Item Citations and Data
Rights
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.