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Subgraph of compatible action graph for finite cyclic groups of p-power order

Shahoodh, Mohammed Khalid and Mohd Sham, Mohamad and Yuhani, Yusof and Sahimel Azwal, Sulaiman and Adam Shariff Adli, Aminuddin (2018) Subgraph of compatible action graph for finite cyclic groups of p-power order. In: International Conference On Mathematical Sciences And Technology 2018 (MATHTECH 2018), 10 -12 Disember 2018 , Hotel Equatorial Penang, Malaysia. pp. 1-8.. (Unpublished)

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Abstract

Given two groups G and H, then the nonabelian tensor product GH is the group generated by gh satisfying the relations ()()gggghghgh′′⊗=⊗⊗and()()hhghhghgh′′ for all ,ggG′∈ and ,hhH′∈. If G and H act on each other and each of which acts on itself by conjugation and satisfying 1() (())ghghggg−′′= and 1() (())hghghhh−′′=, then the actions are said to be compatible. The action of G on H, gh is a homomorphism from G to a group of automorphism H. If (,g)ghh be a pair of the compatible actions for the nonabelian tensor product of GH, then GHGH GHEΓ is a compatible action graph with the set of vertices, ()GHVΓ and the set of edges, ()GHEΓ. In this paper, the necessary and sufficient conditions for the cyclic subgroups ofp-power order acting on each other in a compatible way are given. Hence, a subgraph of a compatible action graph is introduced and its properties are given.

Item Type: Conference or Workshop Item (Lecture)
Uncontrolled Keywords: Algebraic structure; Graph theory
Subjects: L Education > LB Theory and practice of education > LB2300 Higher Education
Q Science > QA Mathematics
Faculty/Division: Faculty of Industrial Sciences And Technology
Depositing User: Pn. Hazlinda Abd Rahman
Date Deposited: 19 Sep 2019 01:40
Last Modified: 19 Sep 2019 01:40
URI: http://umpir.ump.edu.my/id/eprint/24330
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