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...
Saved in:
| Main Author: | |
|---|---|
| Format: | Undergraduates Project Papers |
| Language: | en |
| Published: |
2012
|
| Subjects: | |
| Online Access: | http://umpir.ump.edu.my/id/eprint/4577/1/MOHD_SHAM_MOHAMAD_CD6144.pdf http://umpir.ump.edu.my/id/eprint/4577/ |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1831521588911013888 |
|---|---|
| author | Mohd Sham, Mohamad |
| author_facet | Mohd Sham, Mohamad |
| author_sort | Mohd Sham, Mohamad |
| building | UMPSA Library |
| collection | Institutional Repository |
| content_provider | Universiti Malaysia Pahang Al-Sultan Abdullah |
| content_source | UMPSA Institutional Repository |
| continent | Asia |
| country | Malaysia |
| 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 |
| format | Undergraduates Project Papers |
| id | my.ump.umpir.4577 |
| institution | Universiti Malaysia Pahang |
| language | en |
| publishDate | 2012 |
| record_format | eprints |
| spelling | my.ump.umpir.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/4577/1/MOHD_SHAM_MOHAMAD_CD6144.pdf http://umpir.ump.edu.my/id/eprint/4577/ |
| url_provider | http://umpir.ump.edu.my/ |