On the commutativity degree of metacyclic groups of 5-power order using conjugation action (Malaysian Journal of Fundamental and Applied Sciences, 2017)
An extension of the concept of commutativity degree named the probability that an element of a group fixes a set was introduced in 2013. Suppose is a metacyclic 5-group  and  is the set of all ordered pairs  (x,y) in G*G  such that lcm(|x|,|y|)=5, xy=yx  and x is not equal to y. In this paper, the probability that an element of a metacyclic 5-group fixes the set  is computed by using conjugation action.
Keywords: Commutativity degree; metacyclic 5-groups; conjugation action