The conjugation degree on a set of metacyclic 3-groups

• Main Authors: Amzee Zamri, Siti Norziahidayu, Sarmin, Nor Haniza, El-Sanfaz, Mustafa Anis, Nawi, Adnin Afifi
• Format: Article
• Language: English
• Published: Penerbit UTM Press 2020
• Subjects: QA Mathematics
• Online Access: http://eprints.utm.my/id/eprint/93467/1/NorHanizaSarmin2020_TheConjugationDegreeonaSetofMetacyclic.pdf; http://eprints.utm.my/id/eprint/93467/; https://mjfas.utm.my/index.php/mjfas/article/view/1925
• Institution: Universiti Teknologi 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 Ωis 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.