Number of Compatible Pair for Nontrivial Actions of Finite Cyclic 2-Groups - Sahimel Azwal, Sulaiman; Mohd Sham, Mohamad; Yuhani, Yusof; Mohammed Khalid, Shahoodh (Universiti Teknologi Malaysia, 2016)
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 action act compatibly on each other. The compatible pair for nontrivial actions for finite cyclic 2-groups can be found by using the necessary and sufficient conditions of two finite cyclic 2-groups act compatibly on each other. Hence, the exact number of compatible pair of nontrivial actions for finite cyclic 2-groups are computed and given as a main result in this paper.