The probability of nth degree for some nonabelian metabelian groups
A group G is metabelian if and only if there exists an abelian normal subgroup, A such that the factor group, G/A is abelian. For any group G, the commutativity degree of G is the probability that two randomly selected elements in the group commute and denoted as P(G). Furthermore, the probability o...
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| Format: | Conference or Workshop Item |
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2013
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| author | Abd. Halim, Z. Mohd. Ali, N. M. |
| author_facet | Abd. Halim, Z. Mohd. Ali, N. M. |
| author_sort | Abd. Halim, Z. |
| collection | ePrints |
| description | A group G is metabelian if and only if there exists an abelian normal subgroup, A such that the factor group, G/A is abelian. For any group G, the commutativity degree of G is the probability that two randomly selected elements in the group commute and denoted as P(G). Furthermore, the probability of nth degree of a group G, Pn(G) is defined as the probability that the nth power of a random element commutes with another random element of the same group. It is also known as the nth commutativity degree of a group. In this paper, P(G) and Pn(G) for some nonabelian metabelian groups are determined. |
| first_indexed | 2024-03-05T19:29:59Z |
| format | Conference or Workshop Item |
| id | utm.eprints-51366 |
| institution | Universiti Teknologi Malaysia - ePrints |
| last_indexed | 2024-03-05T19:29:59Z |
| publishDate | 2013 |
| record_format | dspace |
| spelling | utm.eprints-513662017-09-18T01:46:28Z http://eprints.utm.my/51366/ The probability of nth degree for some nonabelian metabelian groups Abd. Halim, Z. Mohd. Ali, N. M. Q Science A group G is metabelian if and only if there exists an abelian normal subgroup, A such that the factor group, G/A is abelian. For any group G, the commutativity degree of G is the probability that two randomly selected elements in the group commute and denoted as P(G). Furthermore, the probability of nth degree of a group G, Pn(G) is defined as the probability that the nth power of a random element commutes with another random element of the same group. It is also known as the nth commutativity degree of a group. In this paper, P(G) and Pn(G) for some nonabelian metabelian groups are determined. 2013 Conference or Workshop Item PeerReviewed Abd. Halim, Z. and Mohd. Ali, N. M. (2013) The probability of nth degree for some nonabelian metabelian groups. In: AIP Conference Proceedings. http://dx.doi.org/10.1063/1.4801213 |
| spellingShingle | Q Science Abd. Halim, Z. Mohd. Ali, N. M. The probability of nth degree for some nonabelian metabelian groups |
| title | The probability of nth degree for some nonabelian metabelian groups |
| title_full | The probability of nth degree for some nonabelian metabelian groups |
| title_fullStr | The probability of nth degree for some nonabelian metabelian groups |
| title_full_unstemmed | The probability of nth degree for some nonabelian metabelian groups |
| title_short | The probability of nth degree for some nonabelian metabelian groups |
| title_sort | probability of nth degree for some nonabelian metabelian groups |
| topic | Q Science |
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