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

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...

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Main Authors:	Shahoodh, Mohammed Khalid, Mohd Sham, Mohamad, Yuhani, Yusof, Sahimel Azwal, Sulaiman, Adam Shariff Adli, Aminuddin
Format:	Conference or Workshop Item
Language:	English English
Published:	Universiti Malaysia Pahang 2018
Subjects:	LB2300 Higher Education QA Mathematics
Online Access:	http://umpir.ump.edu.my/id/eprint/24330/ http://umpir.ump.edu.my/id/eprint/24330/1/53.%20Subgraph%20of%20compatible%20action%20graph%20for%20finite.pdf http://umpir.ump.edu.my/id/eprint/24330/2/53.1%20Subgraph%20of%20compatible%20action%20graph%20for%20finite.pdf

id	ump-24330
recordtype	eprints
spelling	ump-243302019-09-19T01:40:17Z http://umpir.ump.edu.my/id/eprint/24330/ Subgraph of compatible action graph for finite cyclic groups of p-power order Shahoodh, Mohammed Khalid Mohd Sham, Mohamad Yuhani, Yusof Sahimel Azwal, Sulaiman Adam Shariff Adli, Aminuddin LB2300 Higher Education QA Mathematics 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. Universiti Malaysia Pahang 2018-10 Conference or Workshop Item PeerReviewed pdf en http://umpir.ump.edu.my/id/eprint/24330/1/53.%20Subgraph%20of%20compatible%20action%20graph%20for%20finite.pdf pdf en http://umpir.ump.edu.my/id/eprint/24330/2/53.1%20Subgraph%20of%20compatible%20action%20graph%20for%20finite.pdf 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)
repository_type	Digital Repository
institution_category	Local University
institution	Universiti Malaysia Pahang
building	UMP Institutional Repository
collection	Online Access
language	English English
topic	LB2300 Higher Education QA Mathematics
spellingShingle	LB2300 Higher Education QA Mathematics Shahoodh, Mohammed Khalid Mohd Sham, Mohamad Yuhani, Yusof Sahimel Azwal, Sulaiman Adam Shariff Adli, Aminuddin Subgraph of compatible action graph for finite cyclic groups of p-power order
description	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.
format	Conference or Workshop Item
author	Shahoodh, Mohammed Khalid Mohd Sham, Mohamad Yuhani, Yusof Sahimel Azwal, Sulaiman Adam Shariff Adli, Aminuddin
author_facet	Shahoodh, Mohammed Khalid Mohd Sham, Mohamad Yuhani, Yusof Sahimel Azwal, Sulaiman Adam Shariff Adli, Aminuddin
author_sort	Shahoodh, Mohammed Khalid
title	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_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_sort	subgraph of compatible action graph for finite cyclic groups of p-power order
publisher	Universiti Malaysia Pahang
publishDate	2018
url	http://umpir.ump.edu.my/id/eprint/24330/ http://umpir.ump.edu.my/id/eprint/24330/1/53.%20Subgraph%20of%20compatible%20action%20graph%20for%20finite.pdf http://umpir.ump.edu.my/id/eprint/24330/2/53.1%20Subgraph%20of%20compatible%20action%20graph%20for%20finite.pdf
first_indexed	2023-09-18T22:36:45Z
last_indexed	2023-09-18T22:36:45Z
_version_	1777416646461227008

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

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