The relative commutativity degree and sub-multiplicative degree for noncyclic subgroups of some nonabelian metabelian groups

A metabelian group is a group G that has at least an abelian normal subgroup N such that the quotient group G/n is also abelian. The concept of commutativity degree plays an im portant role in determining the abelianness of the group. This concept has been extended to the relative commutativity degr...

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Main Author:	Abu Bakar, Fadhilah
Format:	Thesis
Language:	English
Published:	2017
Subjects:	Q Science (General)
Online Access:	http://eprints.utm.my/id/eprint/78563/1/FadhilahAbuBakarMFS2017.pdf
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id	my-utm-ep.78563
record_format	uketd_dc
spelling	my-utm-ep.785632018-08-29T07:31:55Z The relative commutativity degree and sub-multiplicative degree for noncyclic subgroups of some nonabelian metabelian groups 2017-04 Abu Bakar, Fadhilah Q Science (General) A metabelian group is a group G that has at least an abelian normal subgroup N such that the quotient group G/n is also abelian. The concept of commutativity degree plays an im portant role in determining the abelianness of the group. This concept has been extended to the relative commutativity degree of a subgroup H of a group G which is defined as the probability that an element of H commutes with an element of G. This notion is further extended to the notion of the multiplicative degree of a group G which is defined as the probability that the product of a pair of elements chosen randomly from a group G is in the given subgroup of H . By using those two definitions with an assistance from Groups, Algorithms and Programm ing and Maple software, the relative commutativity degree and sub-multiplicative degree for noncyclic subgroups of nonabelian metabelian groups of order less than 24 and dihedral groups of order at most 24 are determined in this dissertation. 2017-04 Thesis http://eprints.utm.my/id/eprint/78563/ http://eprints.utm.my/id/eprint/78563/1/FadhilahAbuBakarMFS2017.pdf application/pdf en public http://dms.library.utm.my:8080/vital/access/manager/Repository/vital:108575? masters Universiti Teknologi Malaysia, Faculty of Science Faculty of Science
institution	Universiti Teknologi Malaysia
collection	UTM Institutional Repository
language	English
topic	Q Science (General)
spellingShingle	Q Science (General) Abu Bakar, Fadhilah The relative commutativity degree and sub-multiplicative degree for noncyclic subgroups of some nonabelian metabelian groups
description	A metabelian group is a group G that has at least an abelian normal subgroup N such that the quotient group G/n is also abelian. The concept of commutativity degree plays an im portant role in determining the abelianness of the group. This concept has been extended to the relative commutativity degree of a subgroup H of a group G which is defined as the probability that an element of H commutes with an element of G. This notion is further extended to the notion of the multiplicative degree of a group G which is defined as the probability that the product of a pair of elements chosen randomly from a group G is in the given subgroup of H . By using those two definitions with an assistance from Groups, Algorithms and Programm ing and Maple software, the relative commutativity degree and sub-multiplicative degree for noncyclic subgroups of nonabelian metabelian groups of order less than 24 and dihedral groups of order at most 24 are determined in this dissertation.
format	Thesis
qualification_level	Master's degree
author	Abu Bakar, Fadhilah
author_facet	Abu Bakar, Fadhilah
author_sort	Abu Bakar, Fadhilah
title	The relative commutativity degree and sub-multiplicative degree for noncyclic subgroups of some nonabelian metabelian groups
title_short	The relative commutativity degree and sub-multiplicative degree for noncyclic subgroups of some nonabelian metabelian groups
title_full	The relative commutativity degree and sub-multiplicative degree for noncyclic subgroups of some nonabelian metabelian groups
title_fullStr	The relative commutativity degree and sub-multiplicative degree for noncyclic subgroups of some nonabelian metabelian groups
title_full_unstemmed	The relative commutativity degree and sub-multiplicative degree for noncyclic subgroups of some nonabelian metabelian groups
title_sort	relative commutativity degree and sub-multiplicative degree for noncyclic subgroups of some nonabelian metabelian groups
granting_institution	Universiti Teknologi Malaysia, Faculty of Science
granting_department	Faculty of Science
publishDate	2017
url	http://eprints.utm.my/id/eprint/78563/1/FadhilahAbuBakarMFS2017.pdf
_version_	1747818016025870336

The relative commutativity degree and sub-multiplicative degree for noncyclic subgroups of some nonabelian metabelian groups

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