On the Commutativity Degree of Finite Groups of Order via Degree Equation

Abstract

Commutativity degree is a numerical derivation that carries a lot of information about the structure of finite groups. It measures the extent to which two randomly selected non-identity elements of a group commute. The upper bound for the order of the centre of a finite group were obtained by Cody (2010), while Anna (2010) determined same in terms of degree of commutativity; Jelten et al. (2021) worked on commutativity degree p(G) of finite groups via the class equations. In the present paper, we use the derived group of a group as input and the degree equation as a tool to derive a scheme for the commutativity degree of groups of order which are essentially groups of order with , where is an even prime, , an odd prime such that ; and . With this, we have that p(G) = (|G/| + 3) /|G| as one of our results and discovered that 24 groups satisfy the restrictions given as outlined in our discussion in this paper.