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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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Main Authors: El-Sanfaza, Mustafa Anis, Sarmin, Nor Haniza
Format: Article
Published: Research India Publications 2015
Subjects:
QA Mathematics
Online Access:http://eprints.utm.my/id/eprint/58685/
https://www.ripublication.com/Volume/ijaerv10n15.htm
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spelling my.utm.586852021-12-15T06:51:40Z http://eprints.utm.my/id/eprint/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
institution Universiti Teknologi Malaysia
building UTM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Teknologi Malaysia
content_source UTM Institutional Repository
url_provider http://eprints.utm.my/
topic QA Mathematics
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
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.
format Article
author El-Sanfaza, Mustafa Anis
Sarmin, Nor Haniza
author_facet El-Sanfaza, Mustafa Anis
Sarmin, Nor Haniza
author_sort El-Sanfaza, Mustafa Anis
title 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_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_sort on the probability that an element of metacyclic 2-group of positive type fixes a set and its generalized conjugacy class graph
publisher Research India Publications
publishDate 2015
url http://eprints.utm.my/id/eprint/58685/
https://www.ripublication.com/Volume/ijaerv10n15.htm
_version_ 1720436885081292800
score 13.160551

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