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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2017
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my.utm.785632018-08-29T07:31:55Z http://eprints.utm.my/id/eprint/78563/ The relative commutativity degree and sub-multiplicative degree for noncyclic subgroups of some nonabelian metabelian groups 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 NonPeerReviewed application/pdf en http://eprints.utm.my/id/eprint/78563/1/FadhilahAbuBakarMFS2017.pdf Abu Bakar, Fadhilah (2017) The relative commutativity degree and sub-multiplicative degree for noncyclic subgroups of some nonabelian metabelian groups. Masters thesis, Universiti Teknologi Malaysia, Faculty of Science. http://dms.library.utm.my:8080/vital/access/manager/Repository/vital:108575? |
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Q Science (General) |
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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 |
| 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 |
| publishDate |
2017 |
| url |
http://eprints.utm.my/id/eprint/78563/1/FadhilahAbuBakarMFS2017.pdf http://eprints.utm.my/id/eprint/78563/ http://dms.library.utm.my:8080/vital/access/manager/Repository/vital:108575? |
| _version_ |
1643657937032314880 |
| score |
13.251813 |