The nth commutativity degree of some nonabelian metabelian groups

Abstract

In any group G, if and only if there exists an abelian normal subgroup A such that the factor group, A G is abelian then G is called a metabelian group. For any group G, the degree of abelianness of a group is the probability that two randomly selected elements of the group commute and also known as the commutativity degree and denoted as P(G) . Furthermore, the nth degree of abelianness of a group G is defined as the probability that the nth power of a random element commutes with another random element from the same group known as the nth commutativity degree. In this paper, P(G) and Pn (G) for some nonabelian metabelian groups are presented.