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Compatible actions for finite cyclic groups of p-power order

Shahoodh, Mohammed Khalid (2018) Compatible actions for finite cyclic groups of p-power order. PhD thesis, Universiti Malaysia Pahang.

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Compatible actions for finite cyclic groups of p-power order - Table of contents.pdf - Accepted Version

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Compatible actions for finite cyclic groups of p-power order - Abstract.pdf - Accepted Version

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Compatible actions for finite cyclic groups of p-power order - References.pdf - Accepted Version

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Abstract

The concept of the nonabelian tensor product of groups has its origins in the algebraic K-theory 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 p-power order, where p is an odd prime. This research starts with determining the necessary and sufficient conditions for the actions that have p-power order to be compatible. Then, the number of the automorphisms that have the p-power 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 p-power 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; p-power
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: 02 Jan 2019 02:29
URI: http://umpir.ump.edu.my/id/eprint/23509
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