Cover Image

Some applications of metacyclic 2-groups of negative type

The probability that two random elements commute in a finite group G is the quotient of the number of commuting elements and |G|2. Consider a set S consisting of all subsets of commuting elements of G of size two that are in the form (a,b) where a and b commute and lcm(|a|,|b|)=2. The probability th...

Full description

Saved in:
Bibliographic Details
Main Authors: Saleh Omer, Sanaa Mohamed, Sarmin, Nor Haniza, Erfanian, Ahmad
Format: Article
Published: Thailands Natl Science & Technology Development Agency 2016
Subjects:
Q Science
Online Access:http://eprints.utm.my/id/eprint/66753/
http://dx.doi.org/10.2306/scienceasia1513-1874.2016.42S.001
Tags: Add Tag
No Tags, Be the first to tag this record!
id my.utm.66753
record_format eprints
spelling my.utm.667532017-11-22T00:45:07Z http://eprints.utm.my/id/eprint/66753/ Some applications of metacyclic 2-groups of negative type Saleh Omer, Sanaa Mohamed Sarmin, Nor Haniza Erfanian, Ahmad Q Science The probability that two random elements commute in a finite group G is the quotient of the number of commuting elements and |G|2. Consider a set S consisting of all subsets of commuting elements of G of size two that are in the form (a,b) where a and b commute and lcm(|a|,|b|)=2. The probability that a group element fixes S is the number of orbits under the group action on S divided by |S|. In this paper, the probability that a group element fixes a set S under regular action is found for metacyclic 2-groups of negative type of nilpotency class two and of class at least three. The results obtained from the sizes of the orbits are then applied to the generalized conjugacy class graph. Thailands Natl Science & Technology Development Agency 2016-01-02 Article PeerReviewed Saleh Omer, Sanaa Mohamed and Sarmin, Nor Haniza and Erfanian, Ahmad (2016) Some applications of metacyclic 2-groups of negative type. ScienceAsia, 42 (1). pp. 1-4. ISSN 1513-1874 http://dx.doi.org/10.2306/scienceasia1513-1874.2016.42S.001 DOI:10.2306/scienceasia1513-1874.2016.42S.001
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 Q Science
spellingShingle Q Science
Saleh Omer, Sanaa Mohamed
Sarmin, Nor Haniza
Erfanian, Ahmad
Some applications of metacyclic 2-groups of negative type
description The probability that two random elements commute in a finite group G is the quotient of the number of commuting elements and |G|2. Consider a set S consisting of all subsets of commuting elements of G of size two that are in the form (a,b) where a and b commute and lcm(|a|,|b|)=2. The probability that a group element fixes S is the number of orbits under the group action on S divided by |S|. In this paper, the probability that a group element fixes a set S under regular action is found for metacyclic 2-groups of negative type of nilpotency class two and of class at least three. The results obtained from the sizes of the orbits are then applied to the generalized conjugacy class graph.
format Article
author Saleh Omer, Sanaa Mohamed
Sarmin, Nor Haniza
Erfanian, Ahmad
author_facet Saleh Omer, Sanaa Mohamed
Sarmin, Nor Haniza
Erfanian, Ahmad
author_sort Saleh Omer, Sanaa Mohamed
title Some applications of metacyclic 2-groups of negative type
title_short Some applications of metacyclic 2-groups of negative type
title_full Some applications of metacyclic 2-groups of negative type
title_fullStr Some applications of metacyclic 2-groups of negative type
title_full_unstemmed Some applications of metacyclic 2-groups of negative type
title_sort some applications of metacyclic 2-groups of negative type
publisher Thailands Natl Science & Technology Development Agency
publishDate 2016
url http://eprints.utm.my/id/eprint/66753/
http://dx.doi.org/10.2306/scienceasia1513-1874.2016.42S.001
_version_ 1643655848743927808
score 13.244745

Similar Items