Compatible Pair of Nontrivial Actions for Cyclic Groups of 3-Power Order - Shahoodh, Mohammed Khalid; Mohd Sham, Mohamad; Yuhani, Yusof; Sahimel Azwal, Sulaiman (Universiti Malaysia Pahang, 2016)
A compatible action played an important role before computing the nonabelian tensor product. Number of compatible actions will give the different nonabelian tensor product. Thus, this paper present some exact number of compatible pairs of actions for cyclic groups focusing on groups of 3-power order. Some necessary and sufficient number theoretical conditions for a pair of cyclic groups of p-power order with nontrivial actions act compatibly on each other are applied to find the exact number of compatible pairs of actions. Group, Algorithm and Programming (GAP) software is used to find some examples on a different case. Results on the compatible pair of nontrivial actions of order three and nine are given.