On the probability that an element of metacyclic 2-group of positive type fixes a set and its generalized conjugacy class graph
The probability that an element of a group fixes a set is considered as one of the extensions of commutativity degree that can be obtained by some group actions on a set. We denote G as a metacyclic 2-group of positive type of nilpotency of class at least three and O as the set of all subsets of all...
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Research India Publications
2015
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author | El-Sanfaza, Mustafa Anis Sarmin, Nor Haniza |
author_facet | El-Sanfaza, Mustafa Anis Sarmin, Nor Haniza |
author_sort | El-Sanfaza, Mustafa Anis |
collection | ePrints |
description | The probability that an element of a group fixes a set is considered as one of the extensions of commutativity degree that can be obtained by some group actions on a set. We denote G as a metacyclic 2-group of positive type of nilpotency of class at least three and O as the set of all subsets of all commuting elements of G of size two in the form of a,b , where a and b commute and each of order two. In this paper, we compute the probability that an element of G fixes a set in which G acts regularly on O. Then the results are applied to graph theory, more precisely to generalized conjugacy class graph. |
first_indexed | 2024-03-05T19:43:09Z |
format | Article |
id | utm.eprints-58685 |
institution | Universiti Teknologi Malaysia - ePrints |
last_indexed | 2024-03-05T19:43:09Z |
publishDate | 2015 |
publisher | Research India Publications |
record_format | dspace |
spelling | utm.eprints-586852021-12-15T06:51:40Z http://eprints.utm.my/58685/ On the probability that an element of metacyclic 2-group of positive type fixes a set and its generalized conjugacy class graph El-Sanfaza, Mustafa Anis Sarmin, Nor Haniza QA Mathematics The probability that an element of a group fixes a set is considered as one of the extensions of commutativity degree that can be obtained by some group actions on a set. We denote G as a metacyclic 2-group of positive type of nilpotency of class at least three and O as the set of all subsets of all commuting elements of G of size two in the form of a,b , where a and b commute and each of order two. In this paper, we compute the probability that an element of G fixes a set in which G acts regularly on O. Then the results are applied to graph theory, more precisely to generalized conjugacy class graph. Research India Publications 2015 Article PeerReviewed El-Sanfaza, Mustafa Anis and Sarmin, Nor Haniza (2015) On the probability that an element of metacyclic 2-group of positive type fixes a set and its generalized conjugacy class graph. Global Journal of Pure and Applied Mathematics, 11 (2). pp. 899-908. ISSN 0973-1245 https://www.ripublication.com/Volume/ijaerv10n15.htm |
spellingShingle | QA Mathematics El-Sanfaza, Mustafa Anis Sarmin, Nor Haniza On the probability that an element of metacyclic 2-group of positive type fixes a set and its generalized conjugacy class graph |
title | On the probability that an element of metacyclic 2-group of positive type fixes a set and its generalized conjugacy class graph |
title_full | On the probability that an element of metacyclic 2-group of positive type fixes a set and its generalized conjugacy class graph |
title_fullStr | On the probability that an element of metacyclic 2-group of positive type fixes a set and its generalized conjugacy class graph |
title_full_unstemmed | On the probability that an element of metacyclic 2-group of positive type fixes a set and its generalized conjugacy class graph |
title_short | On the probability that an element of metacyclic 2-group of positive type fixes a set and its generalized conjugacy class graph |
title_sort | on the probability that an element of metacyclic 2 group of positive type fixes a set and its generalized conjugacy class graph |
topic | QA Mathematics |
work_keys_str_mv | AT elsanfazamustafaanis ontheprobabilitythatanelementofmetacyclic2groupofpositivetypefixesasetanditsgeneralizedconjugacyclassgraph AT sarminnorhaniza ontheprobabilitythatanelementofmetacyclic2groupofpositivetypefixesasetanditsgeneralizedconjugacyclassgraph |