*The Number of Compatible Pair of Actions for Cyclic Groups of 2-Power Order*

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

The nonabelian tensor product of groups has its origins in the algebraic K-theory and homotopy theory. The nonabelian tensor product for a pair of groups is defined when the actions act compatibly on each other. This research is to determine the maximum number of a compatible pair of actions can be identified between two cyclic groups of 2-power order for nonabelian tensor product. The compatible pair of actions between two cyclic groups of 2-power order can be found by using the necessary and sufficient conditions of two cyclic groups of 2-power order act compatibly on each other. Hence, the number of the compatible pair of actions between two cyclic groups of the 2-power order is given.

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

Published: Dec 30, 2017