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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Main Author:	Sahimel Azwal, Sulaiman
Format:	Thesis
Language:	English
Published:	2018
Subjects:	Q Science (General) QA Mathematics
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
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spelling	my-ump-ir.247162023-05-18T04:57:49Z Compatible pairs of actions for finite cyclic 2-groups and the associated compatible action graphs 2018-06 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 http://umpir.ump.edu.my/id/eprint/24716/ 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 pdf en public phd doctoral Universiti Malaysia Pahang Faculty of Industrial Sciences and Technology Mohamad, Mohd Sham
institution	Universiti Malaysia Pahang Al-Sultan Abdullah
collection	UMPSA Institutional Repository
language	English
advisor	Mohamad, Mohd Sham
topic	Q Science (General) QA Mathematics
spellingShingle	Q Science (General) QA Mathematics Sahimel Azwal, Sulaiman Compatible pairs of actions for finite cyclic 2-groups and the associated compatible action graphs
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.
format	Thesis
qualification_name	Doctor of Philosophy (PhD.)
qualification_level	Doctorate
author	Sahimel Azwal, Sulaiman
author_facet	Sahimel Azwal, Sulaiman
author_sort	Sahimel Azwal, Sulaiman
title	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_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_sort	compatible pairs of actions for finite cyclic 2-groups and the associated compatible action graphs
granting_institution	Universiti Malaysia Pahang
granting_department	Faculty of Industrial Sciences and Technology
publishDate	2018
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
_version_	1783732078618083328

Compatible pairs of actions for finite cyclic 2-groups and the associated compatible action graphs

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