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 fixes...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Penerbit UTM Press
2020
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| Subjects: | |
| 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 |
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| Institution: | Universiti Teknologi Malaysia |
| Language: | English |
| Summary: | 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. |
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