In any finite group G, the commutativity degree of G (denoted

by d(G)) is the probability that two randomly chosen elements of G commute.

More generally, for every n ≥ 2 the nth commutativity degree

(denoted by dn...

ABSTRACT: The probability that two random elements commute in a finite group G is the quotient of the number of commuting elements and |G| Consider a set S consisting of all subsets of commuting elements of G of size two ...

In this paper the number of conjugacy classes of G for some non-abelian finite groups is computed. Also, the

commuting probability of , denoted by Pr(G), is obtained. In particular, the commutativity degree of G both in the split...

Let G be a finite non-abelian metacyclic p-group where p is any prime. We compute the exact number of

conjugacy classes and the commutativity degree of G. In particular, we describe the number of conjugacy classes both in the split and non...

the relative commutativity degree d(C,D8), where C is a cyclic maximal subgroup

of D8. A final conjecture is opened for the groups with few nontrivial values of d(C,G)....

for all y 2 Hg.

Moreover, fx; yg is an edge if x or y belong to H and xyn = ynx

or xny = yxn. In fact, the relative n-th commutativity degree,

Pn(H;G) the probability that n-th power of an element of the sub-

group H commutes...

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 ...