Compatible Pair of Actions for Two Same Cyclic Groups of 2-Power Order

• Main Authors: Mohd Sham, Mohamad, Sahimel Azwal, Sulaiman, Yuhani, Yusof, Shahoodh, Mohammed Khalid
• Format: Article
• Language: English
• Published: IOP Publishing 2017
• Subjects: QA Mathematics
• Online Access: http://umpir.ump.edu.my/id/eprint/18777/1/fist-2017-Mohamad-Compatible%20Pair%20of%20Actions%20for%20Two%20Same.pdf; http://umpir.ump.edu.my/id/eprint/18777/; http://dx.doi.org/10.1088/1742-6596/890/1/012120

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.