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 K-theory 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. Therefore, the...
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| Format: | Thesis |
| Language: | English |
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2018
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| Online Access: | http://umpir.ump.edu.my/id/eprint/23509/1/Compatible%20actions%20for%20finite%20cyclic%20groups%20of%20p-power%20order.wm.pdf |
| _version_ | 1825812457206054912 |
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| author | Shahoodh, Mohammed Khalid |
| author_facet | Shahoodh, Mohammed Khalid |
| author_sort | Shahoodh, Mohammed Khalid |
| collection | UMP |
| description | The concept of the nonabelian tensor product of groups has its origins in the algebraic K-theory 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. Therefore, 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 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. Then, some properties of the compatible action graph are also presented. |
| first_indexed | 2024-03-06T12:29:26Z |
| format | Thesis |
| id | UMPir23509 |
| institution | Universiti Malaysia Pahang |
| language | English |
| last_indexed | 2024-03-06T12:29:26Z |
| publishDate | 2018 |
| record_format | dspace |
| spelling | UMPir235092023-05-18T04:53:26Z http://umpir.ump.edu.my/id/eprint/23509/ Compatible actions for finite cyclic groups of p-power order Shahoodh, Mohammed Khalid QA Mathematics The concept of the nonabelian tensor product of groups has its origins in the algebraic K-theory 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. Therefore, 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 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. Then, some properties of the compatible action graph are also presented. 2018-03 Thesis NonPeerReviewed pdf en http://umpir.ump.edu.my/id/eprint/23509/1/Compatible%20actions%20for%20finite%20cyclic%20groups%20of%20p-power%20order.wm.pdf Shahoodh, Mohammed Khalid (2018) Compatible actions for finite cyclic groups of p-power order. PhD thesis, Universiti Malaysia Pahang (Contributors, Thesis advisor: Mohamad, Mohd Sham). |
| spellingShingle | QA Mathematics Shahoodh, Mohammed Khalid 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/23509/1/Compatible%20actions%20for%20finite%20cyclic%20groups%20of%20p-power%20order.wm.pdf |
| work_keys_str_mv | AT shahoodhmohammedkhalid compatibleactionsforfinitecyclicgroupsofppowerorder |