Compatible Pair of Nontrivial Actions for Some Cyclic Groups of 2-Power Order - Sahimel Azwal, Sulaiman; Mohd Sham, Mohamad; Yuhani, Yusof (2015)
Compatible action played a very important verification before the nonabelian tensor product can be computed. This paper gives the some exact number of compatible pairs of actions for some cyclic groups of 2-power order. Some necessary and sufficient number theoretical conditions for a pair of cyclic groups of 2-power order with nontrivial actions act compatibly on each other are used to investigate some properties to find the exact number of compatible pairs of actions. Algorithms in Groups, Algorithms and Programming (GAP) software are constructed to create more examples on selected case. New results on compatible pair of nontrivial actions of order two and four are given.