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The nonabelian tensor square of a crystallographic group with quaternion point group of order eight

A crystallographic group is a discrete subgroup of the set of isometries of Euclidean space where the quotient space is compact. A torsion free crystallographic group, or also known as a Bieberbach group has the symmetry structure that will reveal its algebraic properties. One of the algebraic prope...

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Main Authors: Mohammad, Siti Afiqah, Sarmin, Nor Haniza, Mat Hassim, Hazzirah Izzati
Format: Conference or Workshop Item
Language:English
Published: 2017
Subjects:
QA Mathematics
Online Access:http://eprints.utm.my/id/eprint/97251/1/SitiAfiqahMohammad2017_TheNonabelianTensorSquare.pdf
http://eprints.utm.my/id/eprint/97251/
http://dx.doi.org/10.1088/1742-6596/893/1/012006
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spelling my.utm.972512022-09-23T04:32:47Z http://eprints.utm.my/id/eprint/97251/ The nonabelian tensor square of a crystallographic group with quaternion point group of order eight Mohammad, Siti Afiqah Sarmin, Nor Haniza Mat Hassim, Hazzirah Izzati QA Mathematics A crystallographic group is a discrete subgroup of the set of isometries of Euclidean space where the quotient space is compact. A torsion free crystallographic group, or also known as a Bieberbach group has the symmetry structure that will reveal its algebraic properties. One of the algebraic properties is its nonabelian tensor square. The nonabelian tensor square is a special case of the nonabelian tensor product where the product is defined if the two groups act on each other in a compatible way and their action is taken to be conjugation. Meanwhile, Bieberbach group with quaternion point group of order eight is a polycyclic group. In this paper, by using the polycyclic method, the computation of the nonabelian tensor square of this group will be shown. 2017 Conference or Workshop Item PeerReviewed application/pdf en http://eprints.utm.my/id/eprint/97251/1/SitiAfiqahMohammad2017_TheNonabelianTensorSquare.pdf Mohammad, Siti Afiqah and Sarmin, Nor Haniza and Mat Hassim, Hazzirah Izzati (2017) The nonabelian tensor square of a crystallographic group with quaternion point group of order eight. In: Asian Mathematical Conference 2016, AMC 2016, 25 - 29 July 2016, Nusa Dua, Bali. http://dx.doi.org/10.1088/1742-6596/893/1/012006
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
Mohammad, Siti Afiqah
Sarmin, Nor Haniza
Mat Hassim, Hazzirah Izzati
The nonabelian tensor square of a crystallographic group with quaternion point group of order eight
description A crystallographic group is a discrete subgroup of the set of isometries of Euclidean space where the quotient space is compact. A torsion free crystallographic group, or also known as a Bieberbach group has the symmetry structure that will reveal its algebraic properties. One of the algebraic properties is its nonabelian tensor square. The nonabelian tensor square is a special case of the nonabelian tensor product where the product is defined if the two groups act on each other in a compatible way and their action is taken to be conjugation. Meanwhile, Bieberbach group with quaternion point group of order eight is a polycyclic group. In this paper, by using the polycyclic method, the computation of the nonabelian tensor square of this group will be shown.
format Conference or Workshop Item
author Mohammad, Siti Afiqah
Sarmin, Nor Haniza
Mat Hassim, Hazzirah Izzati
author_facet Mohammad, Siti Afiqah
Sarmin, Nor Haniza
Mat Hassim, Hazzirah Izzati
author_sort Mohammad, Siti Afiqah
title The nonabelian tensor square of a crystallographic group with quaternion point group of order eight
title_short The nonabelian tensor square of a crystallographic group with quaternion point group of order eight
title_full The nonabelian tensor square of a crystallographic group with quaternion point group of order eight
title_fullStr The nonabelian tensor square of a crystallographic group with quaternion point group of order eight
title_full_unstemmed The nonabelian tensor square of a crystallographic group with quaternion point group of order eight
title_sort nonabelian tensor square of a crystallographic group with quaternion point group of order eight
publishDate 2017
url http://eprints.utm.my/id/eprint/97251/1/SitiAfiqahMohammad2017_TheNonabelianTensorSquare.pdf
http://eprints.utm.my/id/eprint/97251/
http://dx.doi.org/10.1088/1742-6596/893/1/012006
_version_ 1745562357602451456
score 13.160551

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