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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| Format: | Thesis |
| Language: | English |
| Published: |
2017
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| Subjects: | |
| Online Access: | 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? |
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| Summary: | 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. |
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