02207nam a2200265 a 4500 vtls000063759 KUKTEM 20251114204519.0 120919t2012 my a f m 000 0 eng d THE0002035(Local) 201905131614 yusri 201209191258 ida 201209191250 ida UMP QA612.7 .S53 2012 rs Thesis Mohd Sham Mohamad Compatibility conditions and nonabelian tensor products of finite cyclic groups of ρ-power order / Mohd Sham Mohamad Skudai, Johor : Universiti Teknologi Malaysia, 2012 xii, 78 p. : ill. ; 30 cm. + 1 CD-ROM 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 Homotopy theory Non-Abelion groups Finite groups 0 0 lcc 0 1 10000 10000 2019-09-04 0 QA612.7 .S53 2012 rs Thesis 0000065898 2019-09-04 00:00:00 1 2019-09-04 THESIS 0 0 lcc 0 1 10000 10000 2019-09-04 0 CD 6144 | QA612.7 .S53 2012 rs Thesis 0000065899 2019-09-04 00:00:00 1 2019-09-04 THESIS VIRTUA40 3335 3341 VTLSSORT0080*0200*0400*0900*1000*2450*2600*3000*5020*5040*5200*6500*6501*6502*9992