# On the commutativity degree of metacyclic groups of 5-power order using conjugation action

## Authors

• Siti Norziahidayu Amzee Zamri Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Johor
• Nor Haniza Sarmin Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Johor
• Sanhan Muhammad Salih Khasraw Department of Mathematics, College of Education, Salahaddin University-Erbil, Kurdistan Region, Iraq
• Mustafa Anis El-Sanfaz Department of Mathematics, Faculty of Science, University of Benghazi, Libya
• Hamisan Rahmat Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Johor

## Keywords:

Commutativity degree, metacyclic 5-groups, conjugation action

## 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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