Let G be a metacyclic 2-group. The probability that two random elements commute in G is the quotient of the number of commuting elements by the square of the order of G. This concept has been generalized and extended by several authors. One of these extensions is the probability that an element of a group fixes a set, where the set consists 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. In this paper, the probability that a group element fixes a set is found for metacyclic 2-groups of negative type of nilpotency class at least two. The results obtained on the size of the orbits are then applied to graph theory, more precisely to generalized conjugacy class graph.
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22 October 2015
THE 22ND NATIONAL SYMPOSIUM ON MATHEMATICAL SCIENCES (SKSM22): Strengthening Research and Collaboration of Mathematical Sciences in Malaysia
24–26 November 2014
Selangor, Malaysia
Research Article|
October 22 2015
On the probability that a metacyclic 2-group element fixes a set and its generalized conjugacy class graph
N. H. Sarmin;
N. H. Sarmin
aDepartment of Mathematical Sciences, Faculty of Science,
Universiti Teknologi Malaysia
, 81310 UTM Johor Bahru, Johor, Malaysia
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S. M. S. Omer;
S. M. S. Omer
bDepartment of Mathematics, Faculty of Science,
University of Benghazi
, Libya
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A. Erfanian
A. Erfanian
cDepartment of Mathematics and Center of Excellence in Analysis on Algebraic Structures,
Ferdowsi University of Mashhad
, Mashhad, Iran
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AIP Conf. Proc. 1682, 040016 (2015)
Citation
N. H. Sarmin, S. M. S. Omer, A. Erfanian; On the probability that a metacyclic 2-group element fixes a set and its generalized conjugacy class graph. AIP Conf. Proc. 22 October 2015; 1682 (1): 040016. https://doi.org/10.1063/1.4932489
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