Compatible Pair of Actions for Two Same Cyclic Groups of 2-Power Order - Mohd Sham, Mohamad; Sahimel Azwal, Sulaiman; Yuhani, Yusof; Shahoodh, Mohammed Khalid (IOP Publishing, 2017)
The nonabelian tensor product is defined for a pair of groups which act on each other provided the actions satisfying the compatibility conditions. In this paper, the compatible pairs of actions and cyclic groups of the 2-power order are considered. The aim of this study is to investigate the number of the compatible pair of actions for two same cyclic groups of 2-power order with same order of actions. In attained the objectives stated, the necessary and sufficient conditions of cyclic groups of 2-power order act compatibly on each other are used. At the end of this paper, the exact number of compatible pair of actions for two same cyclic groups of 2-power order with a same order of actions is given.