Zakariah, N. A. and Mohd. Ali, N. M. (2021) Relative commutativity degree of nonabelian metabelian groups of order 32. In: 28th Simposium Kebangsaan Sains Matematik, SKSM 2021, 28 July 2021  29 July 2021, Kuantan, Pahang.

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Official URL: http://dx.doi.org/10.1088/17426596/1988/1/012068
Abstract
A metabelian group is a group whose commutator subgroup is abelian. Similarly, 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. The scope of this research is only for nonabelian metabelian groups of order 32. The commutativity degree of a group G is the probability that two elements of the group G (chosen randomly with replacement) commute. This probability can be used to measure how close a group is to be abelian. This concept has been extended to the coprime probability which is defined as the probability of a random pair of elements x and y in G for which the greatest common divisor for the order of x and order of y is equal to one. Furthermore, the study of relative commutativity degree of a subgroup H of a group G which is the probability of an element in H commutes with an element in G is included in this research. Previous researchers have determined the commutativity degree of nonabelian metabelian groups of order at most 32. Meanwhile, the coprime probability and the relative commutativity degree of both cyclic and noncyclic subgroups H are obtained for nonabelian metabelian groups of order at most 30. Since there is no nonabelian group of order 31, thus in this research the coprime probability and the relative commutativity degree of cyclic subgroups for nonabelian metabelian groups of order 32 are determined.
Item Type:  Conference or Workshop Item (Paper) 

Uncontrolled Keywords:  commutativity, greatest common divisors, metabelian groups 
Subjects:  Q Science > QA Mathematics 
Divisions:  Science 
ID Code:  95691 
Deposited By:  Narimah Nawil 
Deposited On:  31 May 2022 13:05 
Last Modified:  31 May 2022 13:05 
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