dc.contributor.advisor |
An, J |
en |
dc.contributor.author |
Doluwe Gedara, Himashela |
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dc.date.accessioned |
2017-10-19T20:41:06Z |
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dc.date.issued |
2017 |
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dc.identifier.uri |
http://hdl.handle.net/2292/36169 |
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dc.description |
Full text is available to authenticated members of The University of Auckland only. |
en |
dc.description.abstract |
Let Gn;m be a nilpotent subgroup of the odd-dimensional orthogonal group of size 2n+2m+1 over a polynomial ring R; where R is an euclidean domain with Char(R) 6= 2: In this thesis, we inspect the structure of Gn;m: We study a decomposition of Gn;m; namely, the semi direct product. Moreover, we find the upper central series of G1;m and G2;m; followed by the upper central series of Gn;m; for any n: We learn that Gn;m has a nilpotency class of 2n - 1; which is a positive odd-integer and independent of m. Then we find that the upper central series and the lower central series of Gn;m coincide, when n = 1. Further, when n = 2; the upper and the lower central series of Gn;m coincide under certain conditions, whereas when n > 2; the upper central series and the lower central series do not coincide. In this thesis, we present abelian subgroups of Gn;m, for each n: Furthermore, we introduce a formula which finds the inverse of a uni-upper triangular matrix over an integral domain. |
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dc.publisher |
ResearchSpace@Auckland |
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dc.relation.ispartof |
Masters Thesis - University of Auckland |
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dc.relation.isreferencedby |
UoA99265061613602091 |
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dc.rights |
Items in ResearchSpace are protected by copyright, with all rights reserved, unless otherwise indicated. Previously published items are made available in accordance with the copyright policy of the publisher. |
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dc.rights |
Restricted Item. Available to authenticated members of The University of Auckland. |
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dc.rights.uri |
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm |
en |
dc.rights.uri |
http://creativecommons.org/licenses/by-nc-sa/3.0/nz/ |
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dc.title |
Structure of Nilpotent Subgroups of the Odd-Dimensional Orthogonal Groups over Polynomial Rings |
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dc.type |
Thesis |
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thesis.degree.discipline |
Mathematics |
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thesis.degree.grantor |
The University of Auckland |
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thesis.degree.level |
Masters |
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dc.rights.holder |
Copyright: The author |
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pubs.elements-id |
697528 |
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pubs.record-created-at-source-date |
2017-10-20 |
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dc.identifier.wikidata |
Q112933625 |
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