Subgraph of Compatible Action Graph for Finite Cyclic Groups of p-Power Order
Given two groups G and H, then the nonabelian tensor product G ⊗ H is the group generated by g ⨂ h satisfying the relations gg' ⊗ h = (gg' ⊗ g h) (g ⨂ h) and g ⊗ hh' = (g ⊗ h) (h g' ⊗ h h) for all g g' ∈ G and h, h' ∈ H. If G and H act on each other and each of which ac...
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| Format: | Conference or Workshop Item |
| Language: | English |
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IOP Publishing
2019
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| Online Access: | http://umpir.ump.edu.my/id/eprint/26994/13/Subgraph%20of%20Compatible%20Action%20Graph%20for%20Finite.pdf |
| _version_ | 1796993790607622144 |
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| author | Shahoodh, Mohammed Khalid Mohd Sham, Mohamad Yuhani, Yusof Sahimel Azwal, Sulaiman |
| author_facet | Shahoodh, Mohammed Khalid Mohd Sham, Mohamad Yuhani, Yusof Sahimel Azwal, Sulaiman |
| author_sort | Shahoodh, Mohammed Khalid |
| collection | UMP |
| description | Given two groups G and H, then the nonabelian tensor product G ⊗ H is the group generated by g ⨂ h satisfying the relations gg' ⊗ h = (gg' ⊗ g h) (g ⨂ h) and g ⊗ hh' = (g ⊗ h) (h g' ⊗ h h) for all g g' ∈ G and h, h' ∈ H. If G and H act on each other and each of which acts on itself by conjugation and satisfying (g h) g' = g(h(g -1 g')) and (h g) h' = h(g(h -1 h')), then the actions are said to be compatible. The action of G on H, g h is a homomorphism from G to a group of automorphism H. If (g h, hg) be a pair of the compatible actions for the nonabelian tensor product of G ⊗ H then Γ G ⊗ H = (V(Γ G ⊗ H ), (E(Γ G ⊗ H )) is a compatible action graph with the set of vertices, (V(Γ G ⊗ H ) and the set of edges, (E(Γ G ⊗ H ). In this paper, the necessary and sufficient conditions for the cyclic subgroups of p-power order acting on each other in a compatible way are given. Hence, a subgra |
| first_indexed | 2024-03-06T12:38:45Z |
| format | Conference or Workshop Item |
| id | UMPir26994 |
| institution | Universiti Malaysia Pahang |
| language | English |
| last_indexed | 2024-03-06T12:38:45Z |
| publishDate | 2019 |
| publisher | IOP Publishing |
| record_format | dspace |
| spelling | UMPir269942020-03-22T23:41:54Z http://umpir.ump.edu.my/id/eprint/26994/ Subgraph of Compatible Action Graph for Finite Cyclic Groups of p-Power Order Shahoodh, Mohammed Khalid Mohd Sham, Mohamad Yuhani, Yusof Sahimel Azwal, Sulaiman T Technology (General) Given two groups G and H, then the nonabelian tensor product G ⊗ H is the group generated by g ⨂ h satisfying the relations gg' ⊗ h = (gg' ⊗ g h) (g ⨂ h) and g ⊗ hh' = (g ⊗ h) (h g' ⊗ h h) for all g g' ∈ G and h, h' ∈ H. If G and H act on each other and each of which acts on itself by conjugation and satisfying (g h) g' = g(h(g -1 g')) and (h g) h' = h(g(h -1 h')), then the actions are said to be compatible. The action of G on H, g h is a homomorphism from G to a group of automorphism H. If (g h, hg) be a pair of the compatible actions for the nonabelian tensor product of G ⊗ H then Γ G ⊗ H = (V(Γ G ⊗ H ), (E(Γ G ⊗ H )) is a compatible action graph with the set of vertices, (V(Γ G ⊗ H ) and the set of edges, (E(Γ G ⊗ H ). In this paper, the necessary and sufficient conditions for the cyclic subgroups of p-power order acting on each other in a compatible way are given. Hence, a subgra IOP Publishing 2019 Conference or Workshop Item PeerReviewed pdf en cc_by http://umpir.ump.edu.my/id/eprint/26994/13/Subgraph%20of%20Compatible%20Action%20Graph%20for%20Finite.pdf Shahoodh, Mohammed Khalid and Mohd Sham, Mohamad and Yuhani, Yusof and Sahimel Azwal, Sulaiman (2019) Subgraph of Compatible Action Graph for Finite Cyclic Groups of p-Power Order. In: Journal of Physics: Conference Series, 2nd International Conference on Applied & Industrial Mathematics and Statistics (ICoAIMS 2019) , 23-25 July 2019 , Kuantan, Pahang, Malaysia. pp. 1-9., 1366 (012064). ISSN 1742-6596 https://doi.org/10.1088/1742-6596/1366/1/012064 |
| spellingShingle | T Technology (General) Shahoodh, Mohammed Khalid Mohd Sham, Mohamad Yuhani, Yusof Sahimel Azwal, Sulaiman Subgraph of Compatible Action Graph for Finite Cyclic Groups of p-Power Order |
| title | Subgraph of Compatible Action Graph for Finite Cyclic Groups of p-Power Order |
| title_full | Subgraph of Compatible Action Graph for Finite Cyclic Groups of p-Power Order |
| title_fullStr | Subgraph of Compatible Action Graph for Finite Cyclic Groups of p-Power Order |
| title_full_unstemmed | Subgraph of Compatible Action Graph for Finite Cyclic Groups of p-Power Order |
| title_short | Subgraph of Compatible Action Graph for Finite Cyclic Groups of p-Power Order |
| title_sort | subgraph of compatible action graph for finite cyclic groups of p power order |
| topic | T Technology (General) |
| url | http://umpir.ump.edu.my/id/eprint/26994/13/Subgraph%20of%20Compatible%20Action%20Graph%20for%20Finite.pdf |
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