| Summary: | The commutativity degree of a finite group G is the probability that two randomly chosen element of the group G commute and is denoted as P(G). The concept of commutativity degree is then extended to the n-th power commutativity degree where it is defined as the probability that the n-th power of a random pair of elements in the group G commute, denoted as Pn(G). Previous study has been found for the case n = 2, called as squared commutativity degree. The notion of a subgroup is added in this paper and new probability has been found, that is the probability that the n-th power of a random pair of elements, one in the subgroup H and another in the group G, commute. The probability is denoted as Pn(H,G) and is obtained for the case n = 2 where it is called the squared relative commutativity degree of a subgroup of a group. The general formula for dihedral groups has been found for this probability. © 2024 Author(s).
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