The probability that an element of a metacyclic 3-group of negative type fixes a set and its orbit graph - Zamri, S. N. A. (American Institute of Physics Inc., 2016)
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.