The conjugation degree on a set of metacyclic 3-groups
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 fi...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Penerbit UTM Press
2020
|
| Subjects: | |
| Online Access: | http://eprints.uthm.edu.my/5618/1/J11467_4ceaae1dfccbd469b8c99ae172ac830d.pdf |
| _version_ | 1796869230304428032 |
|---|---|
| author | Zamri, Siti Norziahidayu Amzee Sarmin, Nor Haniza El-Sanfaz, Mustafa Anis Nawi, Adnin Afifi |
| author_facet | Zamri, Siti Norziahidayu Amzee Sarmin, Nor Haniza El-Sanfaz, Mustafa Anis Nawi, Adnin Afifi |
| author_sort | Zamri, Siti Norziahidayu Amzee |
| collection | UTHM |
| description | 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. |
| first_indexed | 2024-03-05T21:51:45Z |
| format | Article |
| id | uthm.eprints-5618 |
| institution | Universiti Tun Hussein Onn Malaysia |
| language | English |
| last_indexed | 2024-03-05T21:51:45Z |
| publishDate | 2020 |
| publisher | Penerbit UTM Press |
| record_format | dspace |
| spelling | uthm.eprints-56182022-01-17T02:48:34Z http://eprints.uthm.edu.my/5618/ The conjugation degree on a set of metacyclic 3-groups Zamri, Siti Norziahidayu Amzee Sarmin, Nor Haniza El-Sanfaz, Mustafa Anis Nawi, Adnin Afifi QA150-272.5 Algebra 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. Penerbit UTM Press 2020 Article PeerReviewed text en http://eprints.uthm.edu.my/5618/1/J11467_4ceaae1dfccbd469b8c99ae172ac830d.pdf 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 |
| spellingShingle | QA150-272.5 Algebra Zamri, Siti Norziahidayu Amzee Sarmin, Nor Haniza El-Sanfaz, Mustafa Anis Nawi, Adnin Afifi The conjugation degree on a set of metacyclic 3-groups |
| title | The conjugation degree on a set of metacyclic 3-groups |
| title_full | The conjugation degree on a set of metacyclic 3-groups |
| title_fullStr | The conjugation degree on a set of metacyclic 3-groups |
| title_full_unstemmed | The conjugation degree on a set of metacyclic 3-groups |
| title_short | The conjugation degree on a set of metacyclic 3-groups |
| title_sort | conjugation degree on a set of metacyclic 3 groups |
| topic | QA150-272.5 Algebra |
| url | http://eprints.uthm.edu.my/5618/1/J11467_4ceaae1dfccbd469b8c99ae172ac830d.pdf |
| work_keys_str_mv | AT zamrisitinorziahidayuamzee theconjugationdegreeonasetofmetacyclic3groups AT sarminnorhaniza theconjugationdegreeonasetofmetacyclic3groups AT elsanfazmustafaanis theconjugationdegreeonasetofmetacyclic3groups AT nawiadninafifi theconjugationdegreeonasetofmetacyclic3groups AT zamrisitinorziahidayuamzee conjugationdegreeonasetofmetacyclic3groups AT sarminnorhaniza conjugationdegreeonasetofmetacyclic3groups AT elsanfazmustafaanis conjugationdegreeonasetofmetacyclic3groups AT nawiadninafifi conjugationdegreeonasetofmetacyclic3groups |