01953nam a2200217 a 4500001001400000003000700014005001700021008004100038020002200079040000800101100002200109245012300131260005800254300004500312502008700357504002800444520120200472650002001674650002301694650001801717vtls000063759KUKTEM20251114204519.0120919t2012    my a   f m    000 0 eng d  aTHE0002035(Local)  aUMP0 aMohd Sham Mohamad10aCompatibility conditions and nonabelian tensor products of finite cyclic groups of ρ-power order /cMohd Sham Mohamad  aSkudai, Johor :bUniversiti Teknologi Malaysia,c2012  axii, 78 p. :bill. ;c30 cm. +e1 CD-ROM  aThesis (Doctor of Philosophy (Mathematics) -- Universiti Teknologi Malaysia - 2012  aBibliography : p. 65-663 aThe 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 0aHomotopy theory 0aNon-Abelion groups 0aFinite groups