Shahoodh, Mohammed Khalid (2018) Compatible actions for finite cyclic groups of ppower order. PhD thesis, Universiti Malaysia Pahang (Contributors, Thesis advisor: Mohamad, Mohd Sham).

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Abstract
The concept of the nonabelian tensor product of groups has its origins in the algebraic Ktheory and the homotopy theory. This concept is defined on the actions which are compatible to each other. A different compatible pairs of actions can give a different nonabelian tensor products. Therefore, the maximum different nonabelian tensor product depends on the number of compatible pairs of actions. Thus, this research focuses on determining the number of compatible pairs of actions between two finite cyclic groups of ppower order, where p is an odd prime. This research starts with determining the necessary and sufficient conditions for the actions that have ppower order to be compatible. Then, the number of the automorphisms that have the ppower order for such type of groups, which present the actions are found. By the necessary and sufficient conditions, the number of the compatible pairs of actions has been determined according to the order of the action. Furthermore, the compatible action graph and its subgraph were introduced for the finite cyclic groups of ppower order. Then, some properties of the compatible action graph are also presented.
Item Type:  Thesis (PhD) 

Additional Information:  Thesis (Doctor of Philosophy)  Universiti Malaysia Pahang – 2018, SV: DR. MOHD SHAM BIN MOHAMAD, NO. CD: 11374 
Uncontrolled Keywords:  Finite cyclic groups; ppower 
Subjects:  Q Science > QA Mathematics 
Faculty/Division:  Faculty of Industrial Sciences And Technology 
Depositing User:  Mrs. Sufarini Mohd Sudin 
Date Deposited:  02 Jan 2019 02:29 
Last Modified:  18 May 2023 04:53 
URI:  http://umpir.ump.edu.my/id/eprint/23509 
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