Compatible pairs of actions for finite cyclic 2-groups and the associated compatible action graphs
The nonabelian tensor product is defined for a pair of groups which act on each other provided the actions satisfying the compatibility conditions. Different pairs of compatible actions will give different nonabelian tensor products. Thus, in this research, the maximum number of different nonabelian...
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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/24716/1/Compatible%20pairs%20of%20actions%20for%20finite%20cyclic%202-groups%20and%20the%20associated%20compatible%20action%20graphs.wm.pdf |
| _version_ | 1825812660372897792 |
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| author | Sahimel Azwal, Sulaiman |
| author_facet | Sahimel Azwal, Sulaiman |
| author_sort | Sahimel Azwal, Sulaiman |
| collection | UMP |
| description | The nonabelian tensor product is defined for a pair of groups which act on each other provided the actions satisfying the compatibility conditions. Different pairs of compatible actions will give different nonabelian tensor products. Thus, in this research, the maximum number of different nonabelian tensor products between two groups is found by determining the exact number of compatible pairs of actions and focusing only on the finite cyclic 2-groups. This research starts with determination of the exact number of compatible pairs of actions by using the necessary and sufficient conditions of finite cyclic 2-groups to act compatibly on each other. In order to find the number of compatible pairs of actions of finite cyclic 2-groups, the compatible action graph is introduced. Then, some properties of he compatible action graph and a subgraph of the compatible action graph are determined. |
| first_indexed | 2024-03-06T12:32:27Z |
| format | Thesis |
| id | UMPir24716 |
| institution | Universiti Malaysia Pahang |
| language | English |
| last_indexed | 2024-03-06T12:32:27Z |
| publishDate | 2018 |
| record_format | dspace |
| spelling | UMPir247162023-05-18T04:57:49Z http://umpir.ump.edu.my/id/eprint/24716/ Compatible pairs of actions for finite cyclic 2-groups and the associated compatible action graphs Sahimel Azwal, Sulaiman Q Science (General) QA Mathematics The nonabelian tensor product is defined for a pair of groups which act on each other provided the actions satisfying the compatibility conditions. Different pairs of compatible actions will give different nonabelian tensor products. Thus, in this research, the maximum number of different nonabelian tensor products between two groups is found by determining the exact number of compatible pairs of actions and focusing only on the finite cyclic 2-groups. This research starts with determination of the exact number of compatible pairs of actions by using the necessary and sufficient conditions of finite cyclic 2-groups to act compatibly on each other. In order to find the number of compatible pairs of actions of finite cyclic 2-groups, the compatible action graph is introduced. Then, some properties of he compatible action graph and a subgraph of the compatible action graph are determined. 2018-06 Thesis NonPeerReviewed pdf en http://umpir.ump.edu.my/id/eprint/24716/1/Compatible%20pairs%20of%20actions%20for%20finite%20cyclic%202-groups%20and%20the%20associated%20compatible%20action%20graphs.wm.pdf Sahimel Azwal, Sulaiman (2018) Compatible pairs of actions for finite cyclic 2-groups and the associated compatible action graphs. PhD thesis, Universiti Malaysia Pahang (Contributors, Thesis advisor: Mohamad, Mohd Sham). |
| spellingShingle | Q Science (General) QA Mathematics Sahimel Azwal, Sulaiman Compatible pairs of actions for finite cyclic 2-groups and the associated compatible action graphs |
| title | Compatible pairs of actions for finite cyclic 2-groups and the associated compatible action graphs |
| title_full | Compatible pairs of actions for finite cyclic 2-groups and the associated compatible action graphs |
| title_fullStr | Compatible pairs of actions for finite cyclic 2-groups and the associated compatible action graphs |
| title_full_unstemmed | Compatible pairs of actions for finite cyclic 2-groups and the associated compatible action graphs |
| title_short | Compatible pairs of actions for finite cyclic 2-groups and the associated compatible action graphs |
| title_sort | compatible pairs of actions for finite cyclic 2 groups and the associated compatible action graphs |
| topic | Q Science (General) QA Mathematics |
| url | http://umpir.ump.edu.my/id/eprint/24716/1/Compatible%20pairs%20of%20actions%20for%20finite%20cyclic%202-groups%20and%20the%20associated%20compatible%20action%20graphs.wm.pdf |
| work_keys_str_mv | AT sahimelazwalsulaiman compatiblepairsofactionsforfinitecyclic2groupsandtheassociatedcompatibleactiongraphs |