An alternative technique for computing the commutativity degree of dihedral groups

Abstract

Let G be a finite dihedral group Dn. The probability that two random elements commute is called the commutativity degree and it is denoted by P(G). Another technique is used to compute the commutativity is using centralizers. The main purpose of this paper is to construct some upper bounds for the commutativity degree in terms of centralizers for the dihedral group, where the dihedral group acts on itself by conjugation