Mohd Sham Mohamad creator text theses my Skudai, Johor Universiti Teknologi Malaysia 2012 monographic eng

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xii, 78 p. : ill. ; 30 cm. + 1 CD-ROM 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 specialized Mohd Sham Mohamad Thesis (Doctor of Philosophy (Mathematics) -- Universiti Teknologi Malaysia - 2012 Bibliography : p. 65-66 Homotopy theory Non-Abelion groups Finite groups THE0002035(Local) UMP 120919 20251114204519.0 vtls000063759