The Number of Compatible Pair of Actions for Finite Cyclic Groups of 3-Power Order

Mohammed Khalid Shahoodh (University Malaysia Pahang, Kuantan, Malaysia); Mohd Sham Mohamad (Universiti Malaysia Pahang, Malaysia); Yuhani Yusof (Universiti Teknologi Malaysia & Universiti Malaysia PAHANG, Malaysia); Sahimel Azwal Sulaiman (University Malaysia Pahang, Kuantan, Malaysia)

The compatible actions are important in determining the nonabelian tensor product. Different compatible pair of actions gives a different tensor product even for the same group. The purpose of this paper is to determine the exact number of compatible pair of actions for the finite cyclic groups of 3-power order. By using some properties of number theory, the number of the compatible pair of actions for finite cyclic groups of 3-power order with a specific order of actions has been determined and given as a main result in this paper.

Journal: International journal of simulation: systems, science & technology V18

Published: Dec 30, 2017

DOI: 10.5013/IJSSST.a.18.04.01