Compatibility conditions and nonabelian tensor products of finite cyclic groups of Ï-power order
The nonab elian tensor pro ducts of groups originated from a generalized Van Kamp en Theorem and its construction has its origins in algebraic K-theory and in homotopy theory.In this research,cyclic groups of p-p ower order where p is a prime numb er are considered.The aim of this research is to pro...
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| Format: | Undergraduates Project Papers |
| Language: | English |
| Published: |
2012
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| Online Access: | http://umpir.ump.edu.my/id/eprint/4577/ http://umpir.ump.edu.my/id/eprint/4577/ http://umpir.ump.edu.my/id/eprint/4577/1/MOHD_SHAM_MOHAMAD_CD6144.pdf |
| Summary: | The nonab elian tensor pro ducts of groups originated from a generalized Van Kamp en Theorem and its construction has its origins in algebraic K-theory and in homotopy theory.In this research,cyclic groups of p-p ower order where p is a prime numb er are considered.The aim of this research is to prove that the nonabelian tensor pro ducts of some ï¬nite cyclic groups of p-p ower order are cyclic.This research starts with the characterization of automorphisms of cyclic groupsof p-p ower order using numb er theoretical results where the order of the actions are considered.Then,the necessary and sufcient conditions for the actions to b ecompatible are determined for a pair of ï¬nite cyclic groups.Finally,by using a general expansion formula,the nonab elian tensor pro ducts of some cyclic groups of p-p ower order are proven to b e 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 nonab elian tensor product of cyclic groups of 2-power order with two-sided actions and b oth actions have order greater than two have been proven to b e also cyclic |
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