The probability that an element of a metacyclic 3-group of negative type fixes a set and its orbit graph
In this paper, let G be a metacyclic 3-group of negative type of nilpotency class at least three. Let ω be the set of all subsets of commuting elements of G of size three in the form of (a,b), where a and b commute and lcm a , b 3 . The probability that an element of a group G fixes a set ω is consi...
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American Institute of Physics Inc.
2016
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my.utm.732192017-11-28T07:42:36Z http://eprints.utm.my/id/eprint/73219/ The probability that an element of a metacyclic 3-group of negative type fixes a set and its orbit graph Zamri, S. N. A. Sarmin, N. H. Omer, S. M. S. El-Sanfaz, M. A. QA Mathematics In this paper, let G be a metacyclic 3-group of negative type of nilpotency class at least three. Let ω be the set of all subsets of commuting elements of G of size three in the form of (a,b), where a and b commute and lcm a , b 3 . The probability that an element of a group G fixes a set ω is considered as one of the extensions of the commutativity degree that can be obtained under group actions on a set. In this paper, we compute the probability that an element of G fixes a set ωin which G acts on ωby conjugation. The results are then applied to graph theory, more precisely to orbit graph. American Institute of Physics Inc. 2016 Conference or Workshop Item PeerReviewed Zamri, S. N. A. and Sarmin, N. H. and Omer, S. M. S. and El-Sanfaz, M. A. (2016) The probability that an element of a metacyclic 3-group of negative type fixes a set and its orbit graph. In: 23rd Malaysian National Symposium of Mathematical Sciences: Advances in Industrial and Applied Mathematics, SKSM 2015, 24 November 2015 through 26 November 2015, Johor Bahru; Malaysia. https://www.scopus.com/inward/record.uri?eid=2-s2.0-84984586988&doi=10.1063%2f1.4954599&partnerID=40&md5=c8defb91500cdf5a59654795828273dd |
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QA Mathematics Zamri, S. N. A. Sarmin, N. H. Omer, S. M. S. El-Sanfaz, M. A. The probability that an element of a metacyclic 3-group of negative type fixes a set and its orbit graph |
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In this paper, let G be a metacyclic 3-group of negative type of nilpotency class at least three. Let ω be the set of all subsets of commuting elements of G of size three in the form of (a,b), where a and b commute and lcm a , b 3 . The probability that an element of a group G fixes a set ω is considered as one of the extensions of the commutativity degree that can be obtained under group actions on a set. In this paper, we compute the probability that an element of G fixes a set ωin which G acts on ωby conjugation. The results are then applied to graph theory, more precisely to orbit graph. |
| format |
Conference or Workshop Item |
| author |
Zamri, S. N. A. Sarmin, N. H. Omer, S. M. S. El-Sanfaz, M. A. |
| author_facet |
Zamri, S. N. A. Sarmin, N. H. Omer, S. M. S. El-Sanfaz, M. A. |
| author_sort |
Zamri, S. N. A. |
| title |
The probability that an element of a metacyclic 3-group of negative type fixes a set and its orbit graph |
| title_short |
The probability that an element of a metacyclic 3-group of negative type fixes a set and its orbit graph |
| title_full |
The probability that an element of a metacyclic 3-group of negative type fixes a set and its orbit graph |
| title_fullStr |
The probability that an element of a metacyclic 3-group of negative type fixes a set and its orbit graph |
| title_full_unstemmed |
The probability that an element of a metacyclic 3-group of negative type fixes a set and its orbit graph |
| title_sort |
probability that an element of a metacyclic 3-group of negative type fixes a set and its orbit graph |
| publisher |
American Institute of Physics Inc. |
| publishDate |
2016 |
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http://eprints.utm.my/id/eprint/73219/ https://www.scopus.com/inward/record.uri?eid=2-s2.0-84984586988&doi=10.1063%2f1.4954599&partnerID=40&md5=c8defb91500cdf5a59654795828273dd |
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