The nonabelian tensor squares of certain bieberbach groups with cyclic point group of order two

The torsion free crystallographic groups are called Bieberbach groups. These groups are extensions of a finite point group and a free abelian group of finite rank. The rank of the free abelian group is the dimension of Bieberbach group. In this research, Bieberbach groups with cyclic point group of...

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Main Author:	Masri, Rohaidah
Format:	Thesis
Language:	English
Published:	2009
Subjects:	QA Mathematics
Online Access:	http://eprints.utm.my/id/eprint/16980/1/RohaidahMasriPFSA2009.pdf
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id	my-utm-ep.16980
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spelling	my-utm-ep.169802018-10-14T07:23:43Z The nonabelian tensor squares of certain bieberbach groups with cyclic point group of order two 2009 Masri, Rohaidah QA Mathematics The torsion free crystallographic groups are called Bieberbach groups. These groups are extensions of a finite point group and a free abelian group of finite rank. The rank of the free abelian group is the dimension of Bieberbach group. In this research, Bieberbach groups with cyclic point group of order two and Bieberbach groups are elementary abelian 2-group C2xC2 as point group are also considered. These groups are polycyclic since the are extensions of polycyclic groups. Using computational methods developed before for polycyclic groups, the nonabelian tensor squares for these Bieberbach groups with cyclic point group of order two and two Bieberbach groups with the elementary abelian 2-group C2xC2 as point group are given.For the abelian nonabelian tensor square, the formula obtained can be extended to calculate the nonabelian tensor squares of Bieberbach groups of arbitary dimension. For the nonabelian cases, the nonabelian tensor squares of all Bieberbach groups with cyclic point group of order two and elementary abelian 2-group are nilpotent of class two and can be written as a direct product with the nonabelian exterior square as a factor. As a consequence, sufficient conditions for any group such that the nonabelian tensor square is abelian are obtained. 2009 Thesis http://eprints.utm.my/id/eprint/16980/ http://eprints.utm.my/id/eprint/16980/1/RohaidahMasriPFSA2009.pdf application/pdf en public phd doctoral Universiti Teknologi Malaysia, Faculty of Science Faculty of Science
institution	Universiti Teknologi Malaysia
collection	UTM Institutional Repository
language	English
topic	QA Mathematics
spellingShingle	QA Mathematics Masri, Rohaidah The nonabelian tensor squares of certain bieberbach groups with cyclic point group of order two
description	The torsion free crystallographic groups are called Bieberbach groups. These groups are extensions of a finite point group and a free abelian group of finite rank. The rank of the free abelian group is the dimension of Bieberbach group. In this research, Bieberbach groups with cyclic point group of order two and Bieberbach groups are elementary abelian 2-group C2xC2 as point group are also considered. These groups are polycyclic since the are extensions of polycyclic groups. Using computational methods developed before for polycyclic groups, the nonabelian tensor squares for these Bieberbach groups with cyclic point group of order two and two Bieberbach groups with the elementary abelian 2-group C2xC2 as point group are given.For the abelian nonabelian tensor square, the formula obtained can be extended to calculate the nonabelian tensor squares of Bieberbach groups of arbitary dimension. For the nonabelian cases, the nonabelian tensor squares of all Bieberbach groups with cyclic point group of order two and elementary abelian 2-group are nilpotent of class two and can be written as a direct product with the nonabelian exterior square as a factor. As a consequence, sufficient conditions for any group such that the nonabelian tensor square is abelian are obtained.
format	Thesis
qualification_name	Doctor of Philosophy (PhD.)
qualification_level	Doctorate
author	Masri, Rohaidah
author_facet	Masri, Rohaidah
author_sort	Masri, Rohaidah
title	The nonabelian tensor squares of certain bieberbach groups with cyclic point group of order two
title_short	The nonabelian tensor squares of certain bieberbach groups with cyclic point group of order two
title_full	The nonabelian tensor squares of certain bieberbach groups with cyclic point group of order two
title_fullStr	The nonabelian tensor squares of certain bieberbach groups with cyclic point group of order two
title_full_unstemmed	The nonabelian tensor squares of certain bieberbach groups with cyclic point group of order two
title_sort	nonabelian tensor squares of certain bieberbach groups with cyclic point group of order two
granting_institution	Universiti Teknologi Malaysia, Faculty of Science
granting_department	Faculty of Science
publishDate	2009
url	http://eprints.utm.my/id/eprint/16980/1/RohaidahMasriPFSA2009.pdf
_version_	1747815132796289024

The nonabelian tensor squares of certain bieberbach groups with cyclic point group of order two

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