On Generalized Relative Commutativity Degree of Finite Moufang Loop

Abstract

For a given element $g$ of a finite group $G$, the probablility that the commutator of randomly choosen pair elements in $G$ equals $g$ is the relative commutativity degree of $g$. In this paper we are interested in studying the relative commutativity degree of the Dihedral group of order $2n$ and the Quaternion group of order $2^{n}$ for any $n\geq 3$ and we examine the relative commutativity degree of infinite class of the Moufang Loops of Chein type, $M(G,2)$.