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The probability that an element of a metacylic 3-group fixes a set of size three

Siti Norziahidayu Amzee Zamri, Nor Haniza Sarmin, Sanaa Mohamed Saleh Omer

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Abstract

Let G be a metacylic 3-group of negative type of nilpotency class at least three. In this paper, Ω is a set of all subsets of all commuting elements of G of size three in the form of (a,b), where a and b commute. The probability that an element of a group G fixes a set Ω is one of extensions of the commutativity degree that can be obtained under group action on set. This probability is the ratio of the number of orbits to the order of Ω. In this paper, the probability that an element of a group G fixes a set Ω is computed by using conjugate action.

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What this paper is about

Let G be a metacylic 3-group of negative type of nilpotency class at least three. In this paper, Ω is a set of all subsets of all commuting elements of G of size three in the form of (a,b), where a and b commute. The probability that an element of a group G fixes a set Ω is one of extensions of the commutativity degree that can be obtained under group action on set. This probability is the ratio of the number of orbits to the order of Ω. In this paper, the probability that an element of a group G fixes a set Ω is computed by using conjugate action.

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Available abstract

Let G be a metacylic 3-group of negative type of nilpotency class at least three. In this paper, Ω is a set of all subsets of all commuting elements of G of size three in the form of (a,b), where a and b commute. The probability that an element of a group G fixes a set Ω is one of extensions of the commutativity degree that can be obtained under group action on set. This probability is the ratio of the number of orbits to the order of Ω. In this paper, the probability that an element of a group G fixes a set Ω is computed by using conjugate action.

Key concepts: Group (periodic table), Mathematics, Element (criminal law), Commutative property, Set (abstract data type), Combinatorics, Class (philosophy), Discrete mathematics

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