The nth commutativity degree of nonabelian metabelian groups of order at most 24

Abstract

A group G is metabelian if and only if there exists an abelian normal subgroup A such that the factor group, G A is abelian. Meanwhile, for any group G, the commutativity degree of a group is the probability that two randomly selected elements of the group commute and denoted as P(G). Furthermore, the nth commutativity degree 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, Pn(G). In this research, P(G) and Pn(G) for nonabelian metabelian groups of order up to 24 are computed and presented. The nth commutativity degree of a group are found by using the formula of Pn(G).