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
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Abstract
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
| Item Type: | Conference or Workshop Item (Lecture) |
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| Uncontrolled Keywords: | Conjugation; Satisfying; Homomorphism; Finite Cyclic |
| Subjects: | T Technology > T Technology (General) |
| Faculty/Division: | Faculty of Industrial Sciences And Technology Institute of Postgraduate Studies |
| Depositing User: | Pn. Hazlinda Abd Rahman |
| Date Deposited: | 22 Mar 2020 23:41 |
| Last Modified: | 22 Mar 2020 23:41 |
| URI: | http://umpir.ump.edu.my/id/eprint/26994 |
| Download Statistic: | View Download Statistics |
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