TY  - BOOK
AU  - Mohd Sham Mohamad
TI  - Compatibility conditions and nonabelian tensor products of finite cyclic groups of ρ-power order
SN  - THE0002035(Local)
PY  - 2012///
CY  - Skudai, Johor
PB  - Universiti Teknologi Malaysia
KW  - Homotopy theory
KW  - Non-Abelion groups
KW  - Finite groups
N1  - Thesis (Doctor of Philosophy (Mathematics) -- Universiti Teknologi Malaysia - 2012; Bibliography : p. 65-66
N2  - 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
ER  -