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039 9 _a201905131614
_byusri
_c201209191258
_dida
_y201209191250
_zida
040 _aUMP
090 _aQA612.7 .S53 2012 rs Thesis
100 0 _aMohd Sham Mohamad
245 1 0 _aCompatibility conditions and nonabelian tensor products of finite cyclic groups of ρ-power order /
_cMohd Sham Mohamad
260 _aSkudai, Johor :
_bUniversiti Teknologi Malaysia,
_c2012
300 _axii, 78 p. :
_bill. ;
_c30 cm. +
_e1 CD-ROM
502 _aThesis (Doctor of Philosophy (Mathematics) -- Universiti Teknologi Malaysia - 2012
504 _aBibliography : p. 65-66
520 3 _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
650 0 _aHomotopy theory
650 0 _aNon-Abelion groups
650 0 _aFinite groups
999 _aVIRTUA40
_c3335
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