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The n^th Degree of Abelianness 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, 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 . Furthermore, the degree of abelianness of a group G is defined as the probability that the power of a random element commutes with another random element from the same group known as the nth commutativity degree. In this paper, and for some nonabelian metabelian groups are presented.
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