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...
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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.uthm.edu.my/5618/1/J11467_4ceaae1dfccbd469b8c99ae172ac830d.pdf http://eprints.uthm.edu.my/5618/ |
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| Institution: | Universiti Tun Hussein Onn 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 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. |
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