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...

Full description

Saved in:

Bibliographic Details
Main Author:	Fong, Wan Heng
Format:	Thesis
Language:	English
Published:	2004
Subjects:	QA Mathematics
Online Access:	http://eprints.utm.my/id/eprint/7997/1/FongWanHengMFS2004.pdf
Tags:	Add Tag No Tags, Be the first to tag this record!

id	my-utm-ep.7997
record_format	uketd_dc
spelling	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

Some characterizations of groups of order 8

Similar Items