Formulation of the homological functors of some Bieberbach groups with dihedral point group (IR)

The purpose of this research is to produce the formulas of the homological functors of some Bieberbach groups of dimension ?ve with dihedral point group of order eight. The homological functors consist of the nonabelian tensor square, G-trivial subgroup of the nonabelian tensor square, the central s...

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Main Author:	Wan Nor Farhana Wan Mohd Fauzi
Format:	thesis
Language:	eng
Published:	2015
Subjects:	QA Mathematics
Online Access:	https://ir.upsi.edu.my/detailsg.php?det=1026
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spelling	oai:ir.upsi.edu.my:10262020-02-27 Formulation of the homological functors of some Bieberbach groups with dihedral point group (IR) 2015 Wan Nor Farhana Wan Mohd Fauzi QA Mathematics The purpose of this research is to produce the formulas of the homological functors of some Bieberbach groups of dimension ?ve with dihedral point group of order eight. The homological functors consist of the nonabelian tensor square, G-trivial subgroup of the nonabelian tensor square, the central subgroup of the nonabelian tensor square, the nonabelian exterior square and Schur multiplier. The computational method for polycyclic groups is used to determine the formulas of the functors. Selected theorems, lemmas and de?nitions are also used in the computation. The ?findings of this research are the new formulas of the homological functors and also the generalization of one of the functors that is the central subgroup of the nonabelian tensor square. As a conclusion, the nonabelian tensor square and the nonabelian exterior square are found to be not abelian. While G-trivial subgroup of the nonabelian tensor square, the central subgroup of the nonabelian tensor square and Schur multiplier are abelian. The implication of the ?ndings enables the properties of other Bieberbach groups to be explored. In addition, the results can be bene?cial not only to mathematicians in terms of theories and applications but also to chemists and physicists. 2015 thesis https://ir.upsi.edu.my/detailsg.php?det=1026 https://ir.upsi.edu.my/detailsg.php?det=1026 text eng closedAccess Masters Universiti Pendidikan Sultan Idris Fakulti Sains dan Matematik N/A
institution	Universiti Pendidikan Sultan Idris
collection	UPSI Digital Repository
language	eng
topic	QA Mathematics
spellingShingle	QA Mathematics Wan Nor Farhana Wan Mohd Fauzi Formulation of the homological functors of some Bieberbach groups with dihedral point group (IR)
description	The purpose of this research is to produce the formulas of the homological functors of some Bieberbach groups of dimension ?ve with dihedral point group of order eight. The homological functors consist of the nonabelian tensor square, G-trivial subgroup of the nonabelian tensor square, the central subgroup of the nonabelian tensor square, the nonabelian exterior square and Schur multiplier. The computational method for polycyclic groups is used to determine the formulas of the functors. Selected theorems, lemmas and de?nitions are also used in the computation. The ?findings of this research are the new formulas of the homological functors and also the generalization of one of the functors that is the central subgroup of the nonabelian tensor square. As a conclusion, the nonabelian tensor square and the nonabelian exterior square are found to be not abelian. While G-trivial subgroup of the nonabelian tensor square, the central subgroup of the nonabelian tensor square and Schur multiplier are abelian. The implication of the ?ndings enables the properties of other Bieberbach groups to be explored. In addition, the results can be bene?cial not only to mathematicians in terms of theories and applications but also to chemists and physicists.
format	thesis
qualification_name
qualification_level	Master's degree
author	Wan Nor Farhana Wan Mohd Fauzi
author_facet	Wan Nor Farhana Wan Mohd Fauzi
author_sort	Wan Nor Farhana Wan Mohd Fauzi
title	Formulation of the homological functors of some Bieberbach groups with dihedral point group (IR)
title_short	Formulation of the homological functors of some Bieberbach groups with dihedral point group (IR)
title_full	Formulation of the homological functors of some Bieberbach groups with dihedral point group (IR)
title_fullStr	Formulation of the homological functors of some Bieberbach groups with dihedral point group (IR)
title_full_unstemmed	Formulation of the homological functors of some Bieberbach groups with dihedral point group (IR)
title_sort	formulation of the homological functors of some bieberbach groups with dihedral point group (ir)
granting_institution	Universiti Pendidikan Sultan Idris
granting_department	Fakulti Sains dan Matematik
publishDate	2015
url	https://ir.upsi.edu.my/detailsg.php?det=1026
_version_	1747832933147738112

Formulation of the homological functors of some Bieberbach groups with dihedral point group (IR)

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