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

• 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
• Institution: Universiti Teknologi Malaysia

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.