The multiplicative degree of cyclic subgroups of nonabelian metabelian groups of order less than 24

Abstract

A group G is metabelian if and only if there is an abelian normal subgroup N such that the quotient group, GN is abelian. The probability that a random element commutes with another random element in G is called the commutativity degree of a group. Furthermore, the relative commutativity degree of a subgroup H is defined as the probability that a random element of subgroup, H commutes with another random element of a group G. The concept of relative commutativity degree has been extended to the multiplicative degree of a group G, which is defined as the probability that the product of two randomly selected elements from a group G, is in H. In this paper, the multiplicative degree of cyclic subgroups of nonabelian metabelian groups of order less than 24 are determined.