Amzee Zamri, Siti Norziahidayu and Sarmin, Nor Haniza and ElSanfaz, Mustafa Anis and Nawi, Adnin Afifi (2020) The conjugation degree on a set of metacyclic 3groups. Malaysian Journal of Fundamental and Applied Sciences, 16 (5). pp. 530535. ISSN 2289599X

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Official URL: https://mjfas.utm.my/index.php/mjfas/article/view/...
Abstract
Research on commutativity degree has been done by many authors since 1965. The commutativity degree is defined as the probability that two randomly selected elements in a group commute. In this research, an extension of the commutativity degree called the probability that an element of a group fixes a set Ωis explored. The group G in our scope is metacyclic 3group and the set Ω consists of a pair of distinct commuting elements in the group G in which their orders satisfy a certain condition. Meanwhile, the group action used in this research is conjugation. The probability that an element of G fixes a set Ω, defined as the conjugation degree on a set is computed using the number of conjugacy classes. The result turns out to be 7/8 or 1, depending on the orbit and the order of Ω.
Item Type:  Article 

Uncontrolled Keywords:  commutativity degree, conjugation action, conjugation degree, metacyclic groups 
Subjects:  Q Science > QA Mathematics 
Divisions:  Science 
ID Code:  93467 
Deposited By:  Yanti Mohd Shah 
Deposited On:  30 Nov 2021 08:33 
Last Modified:  30 Nov 2021 08:33 
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