Some characterizations of groups of order 8
Group theory is a branch of mathematics which concerns with the study of groups. It has wide applications in other fields too including chemistry. This research focuses on groups of order 8 and their irreducible representations. There are five groups of order 8, namely 0 4 , Q, C8, C2 x C4 and C2 x...
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2004
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my-utm-ep.79972018-09-19T05:07:11Z Some characterizations of groups of order 8 2004-10 Fong, Wan Heng QA Mathematics Group theory is a branch of mathematics which concerns with the study of groups. It has wide applications in other fields too including chemistry. This research focuses on groups of order 8 and their irreducible representations. There are five groups of order 8, namely 0 4 , Q, C8, C2 x C4 and C2 x C2 x C2. For any group, the number of possible representative sets of matrices is infinite, but they can all be reduced to a single fundamental set, called the irreducible representations of the group. Burnside method and Great Orthogonality Theorem method are both used to obtain irreducible representations of all groups of order 8. Then, comparisons of both methods are made. Irreducible representation is actually the nucleus of a character table and is of great importance in chemistry. Groups of order 8 are isomorphic to certain point groups. Point groups are symmetry groups which leave at least one point in space fixed under all operations. In this research, isomorphisms from four out of five groups of order 8, namely 0 4 , C8, C2 x C4 and C2 x C2 x C2, and isomorphisms from proper subgroups of Q to certain point groups are determined. 2004-10 Thesis http://eprints.utm.my/id/eprint/7997/ http://eprints.utm.my/id/eprint/7997/1/FongWanHengMFS2004.pdf application/pdf en public http://dms.library.utm.my:8080/vital/access/manager/Repository/vital:11521 masters Universiti Teknologi Malaysia, Faculty of Science Faculty of Science |
| institution |
Universiti Teknologi Malaysia |
| collection |
UTM Institutional Repository |
| language |
English |
| topic |
QA Mathematics |
| spellingShingle |
QA Mathematics Fong, Wan Heng Some characterizations of groups of order 8 |
| description |
Group theory is a branch of mathematics which concerns with the study of groups. It has wide applications in other fields too including chemistry. This research focuses on groups of order 8 and their irreducible representations. There are five groups of order 8, namely 0 4 , Q, C8, C2 x C4 and C2 x C2 x C2. For any group, the number of possible representative sets of matrices is infinite, but they can all be reduced to a single fundamental set, called the irreducible representations of the group. Burnside method and Great Orthogonality Theorem method are both used to obtain irreducible representations of all groups of order 8. Then, comparisons of both methods are made. Irreducible representation is actually the nucleus of a character table and is of great importance in chemistry. Groups of order 8 are isomorphic to certain point groups. Point groups are symmetry groups which leave at least one point in space fixed under all operations. In this research, isomorphisms from four out of five groups of order 8, namely 0 4 , C8, C2 x C4 and C2 x C2 x C2, and isomorphisms from proper subgroups of Q to certain point groups are determined. |
| format |
Thesis |
| qualification_level |
Master's degree |
| author |
Fong, Wan Heng |
| author_facet |
Fong, Wan Heng |
| author_sort |
Fong, Wan Heng |
| title |
Some characterizations of groups of order 8 |
| title_short |
Some characterizations of groups of order 8 |
| title_full |
Some characterizations of groups of order 8 |
| title_fullStr |
Some characterizations of groups of order 8 |
| title_full_unstemmed |
Some characterizations of groups of order 8 |
| title_sort |
some characterizations of groups of order 8 |
| granting_institution |
Universiti Teknologi Malaysia, Faculty of Science |
| granting_department |
Faculty of Science |
| publishDate |
2004 |
| url |
http://eprints.utm.my/id/eprint/7997/1/FongWanHengMFS2004.pdf |
| _version_ |
1747814717959700480 |