The conjugation degree on a set of metacyclic 3-groups

• Main Authors: Zamri, Siti Norziahidayu Amzee, Sarmin, Nor Haniza, El-Sanfaz, Mustafa Anis, Nawi, Adnin Afifi
• Format: Article
• Language: English
• Published: Penerbit UTM Press 2020
• Subjects: QA150-272.5 Algebra
• Online Access: http://eprints.uthm.edu.my/5618/1/J11467_4ceaae1dfccbd469b8c99ae172ac830d.pdf; http://eprints.uthm.edu.my/5618/
• Institution: Universiti Tun Hussein Onn Malaysia

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.