Compatibility conditions and nonabelian tensor products of finite cyclic groups of ρ-power order / Mohd Sham Mohamad
Material type:
TextPublication details: Skudai, Johor : Universiti Teknologi Malaysia, 2012Description: xii, 78 p. : ill. ; 30 cm. + 1 CD-ROMISBN: - THE0002035(Local)
| Item type | Current library | Call number | Copy number | Status | Date due | Barcode | |
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Thesis
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UMPLIB GAMBANG | QA612.7 .S53 2012 rs Thesis (Browse shelf(Opens below)) | 1 | Not for loan | 0000065898 | ||
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Thesis
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UMPLIB GAMBANG | CD 6144 | QA612.7 .S53 2012 rs Thesis (Browse shelf(Opens below)) | 1 | Not for loan | 0000065899 |
Thesis (Doctor of Philosophy (Mathematics) -- Universiti Teknologi Malaysia - 2012
Bibliography : p. 65-66
The nonabelian tensor pro ducts of groups originated from a generalized Van Kampen Theorem and its construction has its origins in algebraic K-theory and in homotopy theory. In this research, cyclic groups of p -power order where p is a prime number are considered. The aim of this research is to prove that the nonabelian tensor pro ducts of some finite cyclic groups of p -power order are cyclic. This research starts with the characterization of automorphisms of cyclic groups of p -power order using numb er theoretical results where the order of the actions are considered. Then, the necessary and sufficient conditions for the actions to be compatible are determined for a pair of finite cyclic groups. Finally, by using a general expansion formula, the nonabelian tensor products of some cyclic groups of p-power order are proven to be cyclic. The results of this research show that the nonabelian tensor pro duct of cyclic groups of p -p ower order where p is an odd prime with two-sided actions are cyclic. Furthermore, the nonabelian tensor product of cyclic groups of 2-power order with two-sided actions and both actions have order greater than two have been proven to be also cyclic