The relative commutativity degree of noncyclic subgroups of nonabelian metabelian groups of order at most 14

A metabelian group is a group G that have at least an abelian normal subgroup N such that the quotient group G N is also abelian. The concept of commutativity degree plays as important role in determining the abelianness of the group. This concept has been extended to the relative commutativity degree of a subgroup H of a group G which defined as the probability that an element of H commutes with an element of G. In this paper, the relative commutativity degree for noncyclic subgroups of nonabelian metabelian groups of order at most 14 are determined.