Compatibility conditions and nonabelian tensor products of finite cyclic groups of ρ-power order

Mohd Sham, Mohamad (2012) Compatibility conditions and nonabelian tensor products of finite cyclic groups of ρ-power order. Faculty of Science, Universiti Teknologi Malaysia.

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Abstract

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 finite 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 finite 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

Item Type:	Undergraduates Project Papers
Uncontrolled Keywords:	Homotopy theory Non Abelion groups
Subjects:	Q Science > QA Mathematics
Depositing User:	Shamsor Masra Othman
Date Deposited:	16 Dec 2013 03:03
Last Modified:	08 Jul 2021 03:19
URI:	http://umpir.ump.edu.my/id/eprint/4577
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