) 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...

Let G be a finite non-abelian group and let Ω be a set of elements of G. Let A be the set of commuting elements in Ω, i.e A={v∈Ω :vg=gv, g∈G}. In this paper, we extend the work on conjugate graph by defining

a new ...

In this paper, G denotes a metacyclic 2-group of positive type of nilpotency class at least three and

is the set of all subsets of commuting elements of G of size two in the form of (a; b ), where a and b

commute ...