The conjugation degree on a set of metacyclic 3-groups

Zamri, Siti Norziahidayu Amzee and Sarmin, Nor Haniza and El-Sanfaz, Mustafa Anis and Nawi, Adnin Afifi (2020) The conjugation degree on a set of metacyclic 3-groups. Malaysian Journal of Fundamental and Applied Sciences, 16 (5). pp. 530-535. ISSN 2289-5981

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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 Ω is explored. The group G in our scope is metacyclic 3-group 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 > QA150-272.5 Algebra
Divisions:	Center for Diploma Studies > Dept. of Science and Mathematics
Depositing User:	Mr. Abdul Rahim Mat Radzuan
Date Deposited:	17 Jan 2022 02:48
Last Modified:	17 Jan 2022 02:48
URI:	http://eprints.uthm.edu.my/id/eprint/5618

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