Compatible actions for finite cyclic groups of p-power order
The concept of the nonabelian tensor product of groups has its origins in the algebraic Ktheory and the homotopy theory. This concept is defined on the actions which are compatible to each other. A different compatible pairs of actions can give a different nonabelian tensor products. The maximum dif...
| Main Authors: | , , , , , |
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| Format: | Research Report |
| Language: | English |
| Published: |
2020
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| Subjects: | |
| Online Access: | http://umpir.ump.edu.my/id/eprint/36294/1/Compatible%20actions%20for%20finite%20cyclic%20groups%20of%20p-power%20order.wm.pdf |
| _version_ | 1825814719874727936 |
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| author | Mohamad, Mohd Sham Mohd Aziz, Mohd Khairul Bazli Adam, Samsudin Adli Aminuddin, Adam Shariff Yusof, Yuhani Nor Haniza, Sarmin |
| author_facet | Mohamad, Mohd Sham Mohd Aziz, Mohd Khairul Bazli Adam, Samsudin Adli Aminuddin, Adam Shariff Yusof, Yuhani Nor Haniza, Sarmin |
| author_sort | Mohamad, Mohd Sham |
| collection | UMP |
| description | The concept of the nonabelian tensor product of groups has its origins in the algebraic Ktheory and the homotopy theory. This concept is defined on the actions which are compatible to each other. A different compatible pairs of actions can give a different nonabelian tensor products. The maximum different nonabelian tensor product depends on the number of compatible pairs of actions. Thus, this research focuses on determining the number of compatible pairs of actions between two finite cyclic groups of p-power order, where p is an odd prime. This research starts with determining the necessary and sufficient conditions for the actions that have the p-power order to be compatible. Then, the number of the automorphisms that have the p-power order for such type of groups, which present the actions are found. By the necessary and sufficient conditions, the number of the compatible pairs of actions has been determined according to the order of the action. Furthermore, the compatible action graph and its subgraph were introduced for the finite cyclic groups of p-power order, where p is an odd prime. Then, some properties of the compatible action graph are also presented. |
| first_indexed | 2024-03-06T13:02:44Z |
| format | Research Report |
| id | UMPir36294 |
| institution | Universiti Malaysia Pahang |
| language | English |
| last_indexed | 2024-03-06T13:02:44Z |
| publishDate | 2020 |
| record_format | dspace |
| spelling | UMPir362942023-02-13T07:04:21Z http://umpir.ump.edu.my/id/eprint/36294/ Compatible actions for finite cyclic groups of p-power order Mohamad, Mohd Sham Mohd Aziz, Mohd Khairul Bazli Adam, Samsudin Adli Aminuddin, Adam Shariff Yusof, Yuhani Nor Haniza, Sarmin QA Mathematics The concept of the nonabelian tensor product of groups has its origins in the algebraic Ktheory and the homotopy theory. This concept is defined on the actions which are compatible to each other. A different compatible pairs of actions can give a different nonabelian tensor products. The maximum different nonabelian tensor product depends on the number of compatible pairs of actions. Thus, this research focuses on determining the number of compatible pairs of actions between two finite cyclic groups of p-power order, where p is an odd prime. This research starts with determining the necessary and sufficient conditions for the actions that have the p-power order to be compatible. Then, the number of the automorphisms that have the p-power order for such type of groups, which present the actions are found. By the necessary and sufficient conditions, the number of the compatible pairs of actions has been determined according to the order of the action. Furthermore, the compatible action graph and its subgraph were introduced for the finite cyclic groups of p-power order, where p is an odd prime. Then, some properties of the compatible action graph are also presented. 2020 Research Report NonPeerReviewed pdf en http://umpir.ump.edu.my/id/eprint/36294/1/Compatible%20actions%20for%20finite%20cyclic%20groups%20of%20p-power%20order.wm.pdf Mohamad, Mohd Sham and Mohd Aziz, Mohd Khairul Bazli and Adam, Samsudin and Adli Aminuddin, Adam Shariff and Yusof, Yuhani and Nor Haniza, Sarmin (2020) Compatible actions for finite cyclic groups of p-power order. , [Research Report] (Unpublished) |
| spellingShingle | QA Mathematics Mohamad, Mohd Sham Mohd Aziz, Mohd Khairul Bazli Adam, Samsudin Adli Aminuddin, Adam Shariff Yusof, Yuhani Nor Haniza, Sarmin Compatible actions for finite cyclic groups of p-power order |
| title | Compatible actions for finite cyclic groups of p-power order |
| title_full | Compatible actions for finite cyclic groups of p-power order |
| title_fullStr | Compatible actions for finite cyclic groups of p-power order |
| title_full_unstemmed | Compatible actions for finite cyclic groups of p-power order |
| title_short | Compatible actions for finite cyclic groups of p-power order |
| title_sort | compatible actions for finite cyclic groups of p power order |
| topic | QA Mathematics |
| url | http://umpir.ump.edu.my/id/eprint/36294/1/Compatible%20actions%20for%20finite%20cyclic%20groups%20of%20p-power%20order.wm.pdf |
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