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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
http://eprints.utm.my/id/eprint/16980/
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spelling my.utm.169802018-10-14T07:23:43Z http://eprints.utm.my/id/eprint/16980/ The nonabelian tensor squares of certain bieberbach groups with cyclic point group of order two 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 NonPeerReviewed application/pdf en http://eprints.utm.my/id/eprint/16980/1/RohaidahMasriPFSA2009.pdf Masri, Rohaidah (2009) The nonabelian tensor squares of certain bieberbach groups with cyclic point group of order two. PhD thesis, Universiti Teknologi Malaysia, Faculty of Science.
institution Universiti Teknologi Malaysia
building UTM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Teknologi Malaysia
content_source UTM Institutional Repository
url_provider http://eprints.utm.my/
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
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
publishDate 2009
url http://eprints.utm.my/id/eprint/16980/1/RohaidahMasriPFSA2009.pdf
http://eprints.utm.my/id/eprint/16980/
_version_ 1643646693843927040
score 13.211869

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