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 |
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2012
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| Online Access: | http://umpir.ump.edu.my/id/eprint/4577/ http://umpir.ump.edu.my/id/eprint/4577/1/MOHD_SHAM_MOHAMAD_CD6144.pdf |
| _version_ | 1848817417224978432 |
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| author | Mohd Sham, Mohamad |
| author_facet | Mohd Sham, Mohamad |
| author_sort | Mohd Sham, Mohamad |
| building | UMP Institutional Repository |
| collection | Online Access |
| description | 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 |
| first_indexed | 2025-11-15T01:21:26Z |
| format | Undergraduates Project Papers |
| id | ump-4577 |
| institution | Universiti Malaysia Pahang |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T01:21:26Z |
| publishDate | 2012 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | ump-45772021-07-08T03:19:23Z http://umpir.ump.edu.my/id/eprint/4577/ Compatibility conditions and nonabelian tensor products of finite cyclic groups of Ï-power order Mohd Sham, Mohamad QA Mathematics 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 2012-03 Undergraduates Project Papers NonPeerReviewed application/pdf en http://umpir.ump.edu.my/id/eprint/4577/1/MOHD_SHAM_MOHAMAD_CD6144.pdf Mohd Sham, Mohamad (2012) Compatibility conditions and nonabelian tensor products of finite cyclic groups of Ï-power order. Faculty of Science, Universiti Teknologi Malaysia. |
| spellingShingle | QA Mathematics Mohd Sham, Mohamad Compatibility conditions and nonabelian tensor products of finite cyclic groups of Ï-power order |
| title | Compatibility conditions and nonabelian tensor products of finite cyclic groups of Ï-power order |
| title_full | Compatibility conditions and nonabelian tensor products of finite cyclic groups of Ï-power order |
| title_fullStr | Compatibility conditions and nonabelian tensor products of finite cyclic groups of Ï-power order |
| title_full_unstemmed | Compatibility conditions and nonabelian tensor products of finite cyclic groups of Ï-power order |
| title_short | Compatibility conditions and nonabelian tensor products of finite cyclic groups of Ï-power order |
| title_sort | compatibility conditions and nonabelian tensor products of finite cyclic groups of ï-power order |
| topic | QA Mathematics |
| url | http://umpir.ump.edu.my/id/eprint/4577/ http://umpir.ump.edu.my/id/eprint/4577/1/MOHD_SHAM_MOHAMAD_CD6144.pdf |