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: | , , |
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| Format: | Conference or Workshop Item |
| Language: | English |
| Published: |
2017
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| Subjects: | |
| 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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| Summary: | 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. |
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