Abstract
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.
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