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The probability that an element of a metacyclic 3-group of negative type fixes a set and its orbit graph

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.

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Abstract

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.

Item Type:Conference or Workshop Item (Paper)
Uncontrolled Keywords:nilpotency class
Subjects:Q Science > QA Mathematics
Divisions:Science
ID Code:73219
Deposited By: Muhammad Atiff Mahussain
Deposited On:28 Nov 2017 15:42
Last Modified:28 Nov 2017 15:42

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