The commutativity degree of 3-engel groups up to order 40

Friedrich Engel has discovered Engel groups in the 50s in Germany. The origin of this group lies in the theory of Lie algebras. As an example, one of the basic classical results for Engel Lie algebras is Engel’s theorem. In this research, the 3- Engel groups of order up to 40 will be the main focus....

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Main Author:	Zakaria, Mardhiah
Format:	Thesis
Language:	English
Published:	2011
Subjects:	Q Science (General) QA76 Computer software
Online Access:	http://eprints.utm.my/id/eprint/47967/25/MardhiahZakariaMFS2011.pdf
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id	my-utm-ep.47967
record_format	uketd_dc
spelling	my-utm-ep.479672018-05-30T03:57:42Z The commutativity degree of 3-engel groups up to order 40 2011-06 Zakaria, Mardhiah Q Science (General) QA76 Computer software Friedrich Engel has discovered Engel groups in the 50s in Germany. The origin of this group lies in the theory of Lie algebras. As an example, one of the basic classical results for Engel Lie algebras is Engel’s theorem. In this research, the 3- Engel groups of order up to 40 will be the main focus. An application of 3-Engel groups on probability theory will be presented too. The commutativity degree can also be viewed as the probability that two elements in the group commute denoted by . This probability applied to the eighteen 3-Engel groups with order at most 40 is proven to be at most 5/8. A software named Groups, Algorithms and Programming (GAP) software is used to facilitate most of the calculations in this research. 2011-06 Thesis http://eprints.utm.my/id/eprint/47967/ http://eprints.utm.my/id/eprint/47967/25/MardhiahZakariaMFS2011.pdf application/pdf en public masters Universiti Teknologi Malaysia, Faculty of Science Faculty of Science
institution	Universiti Teknologi Malaysia
collection	UTM Institutional Repository
language	English
topic	Q Science (General) QA76 Computer software
spellingShingle	Q Science (General) QA76 Computer software Zakaria, Mardhiah The commutativity degree of 3-engel groups up to order 40
description	Friedrich Engel has discovered Engel groups in the 50s in Germany. The origin of this group lies in the theory of Lie algebras. As an example, one of the basic classical results for Engel Lie algebras is Engel’s theorem. In this research, the 3- Engel groups of order up to 40 will be the main focus. An application of 3-Engel groups on probability theory will be presented too. The commutativity degree can also be viewed as the probability that two elements in the group commute denoted by . This probability applied to the eighteen 3-Engel groups with order at most 40 is proven to be at most 5/8. A software named Groups, Algorithms and Programming (GAP) software is used to facilitate most of the calculations in this research.
format	Thesis
qualification_level	Master's degree
author	Zakaria, Mardhiah
author_facet	Zakaria, Mardhiah
author_sort	Zakaria, Mardhiah
title	The commutativity degree of 3-engel groups up to order 40
title_short	The commutativity degree of 3-engel groups up to order 40
title_full	The commutativity degree of 3-engel groups up to order 40
title_fullStr	The commutativity degree of 3-engel groups up to order 40
title_full_unstemmed	The commutativity degree of 3-engel groups up to order 40
title_sort	commutativity degree of 3-engel groups up to order 40
granting_institution	Universiti Teknologi Malaysia, Faculty of Science
granting_department	Faculty of Science
publishDate	2011
url	http://eprints.utm.my/id/eprint/47967/25/MardhiahZakariaMFS2011.pdf
_version_	1747817275301298176

The commutativity degree of 3-engel groups up to order 40

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