A generalization on the nth commutativity degree of alternating groups of degree 4 and 5

The theory of commutativity degree is important in determining the abelianness of a group. the commutativity degree of a finite group g is the probability that a pair of elements chosen randomly from a group g,commute. the concept of commutativity degree can be generalized to the nth commutativity degree of a group which is defined as the probability of commuting the nth power of a randomly chosen element with another random element from the same group. in this research,the nth commutativity degree of alternating groups of degree 4 and 5 are presented. © 2016 penerbit utm press. all rights reserved.