The commutativity degree of all nonabelian metabelian groups of order at most 24

A metabelian group is a group whose commutator subgroup is abelian. Equivalently, a group G is metabelian if and only if there exists an abelian normal subgroup A such that the quotient group G/A is abelian. Meanwhile, the commutativity degree can be viewed as the probability that two elements in a...

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Main Author:	Che Mohd., Maryaam
Format:	Thesis
Language:	English
Published:	2011
Subjects:	QA Mathematics
Online Access:	http://eprints.utm.my/id/eprint/47965/25/MaryaamCheMohdMFS2011.pdf
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id	my-utm-ep.47965
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spelling	my-utm-ep.479652018-05-30T03:57:40Z The commutativity degree of all nonabelian metabelian groups of order at most 24 2011-06 Che Mohd., Maryaam QA Mathematics A metabelian group is a group whose commutator subgroup is abelian. Equivalently, a group G is metabelian if and only if there exists an abelian normal subgroup A such that the quotient group G/A is abelian. Meanwhile, the commutativity degree can be viewed as the probability that two elements in a group commute, denoted by P(G) . The main objective of this research is to compute the commutativity degree of all metabelian groups of order at most 24. Some basic concepts related with P(G) will first be presented. Two approaches have been used to compute P(G), where G is a metabelian group of order at most 24, namely the 0-1 Table and the Conjugacy Class Method. A software named Groups, Algorithms and Programming (GAP) have been used to facilitate the computations of the commutativity degree. 2011-06 Thesis http://eprints.utm.my/id/eprint/47965/ http://eprints.utm.my/id/eprint/47965/25/MaryaamCheMohdMFS2011.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	QA Mathematics
spellingShingle	QA Mathematics Che Mohd., Maryaam The commutativity degree of all nonabelian metabelian groups of order at most 24
description	A metabelian group is a group whose commutator subgroup is abelian. Equivalently, a group G is metabelian if and only if there exists an abelian normal subgroup A such that the quotient group G/A is abelian. Meanwhile, the commutativity degree can be viewed as the probability that two elements in a group commute, denoted by P(G) . The main objective of this research is to compute the commutativity degree of all metabelian groups of order at most 24. Some basic concepts related with P(G) will first be presented. Two approaches have been used to compute P(G), where G is a metabelian group of order at most 24, namely the 0-1 Table and the Conjugacy Class Method. A software named Groups, Algorithms and Programming (GAP) have been used to facilitate the computations of the commutativity degree.
format	Thesis
qualification_level	Master's degree
author	Che Mohd., Maryaam
author_facet	Che Mohd., Maryaam
author_sort	Che Mohd., Maryaam
title	The commutativity degree of all nonabelian metabelian groups of order at most 24
title_short	The commutativity degree of all nonabelian metabelian groups of order at most 24
title_full	The commutativity degree of all nonabelian metabelian groups of order at most 24
title_fullStr	The commutativity degree of all nonabelian metabelian groups of order at most 24
title_full_unstemmed	The commutativity degree of all nonabelian metabelian groups of order at most 24
title_sort	commutativity degree of all nonabelian metabelian groups of order at most 24
granting_institution	Universiti Teknologi Malaysia, Faculty of Science
granting_department	Faculty of Science
publishDate	2011
url	http://eprints.utm.my/id/eprint/47965/25/MaryaamCheMohdMFS2011.pdf
_version_	1747817274814758912

The commutativity degree of all nonabelian metabelian groups of order at most 24

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