On the Generalization of the Nonabelian Tensor Square of a Bieberbach Group with Symmetric Point Group

Y  T  Tan; N  MohdIdrus; R  Masri; N  H  Sarmin; H  I  Mat Hassim

doi:10.17485/ijst/2016/v9iS1/92736

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On the Generalization of the Nonabelian Tensor Square of a Bieberbach Group with Symmetric Point Group

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Indian Journal of Science and Technology

DOI: 10.17485/ijst/2016/v9iS1/92736

Year: 2016, Volume: 9, Issue: Special Issue 1, Pages: 1-6

Original Article

On the Generalization of the Nonabelian Tensor Square of a Bieberbach Group with Symmetric Point Group

Y. T. Tan¹ , N. MohdIdrus^1*, R. Masri¹ , N. H. Sarmin² , H. I. Mat Hassim²

¹ Faculty of Science and Mathematics, Department of Mathematics, Sultan Idris Education University, Tanjung Malim, Perak Darul Ridzuan 35900, Malaysia; [email protected]
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² Faculty of Science, Department of Mathematical Sciences, Universiti of Technology, Pusat Pentadbiran Universiti Teknologi Malaysia, UTM, 81310 Skudai, Johor Malaysia; [email protected]
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*Author for correspondence
MohdIdrus
Department of Mathematics
Email:[email protected]

This work is licensed under a Creative Commons Attribution 4.0 International License.

Abstract

The nonabelian tensor square is a homological functor which can reveal the properties of a group. Meanwhile, a Bieberbach group with symmetric point group of order six is polycyclic. In this paper, by using the method constructed for polycyclic groups, the nonabelian tensor square of the group is computed and generalized up to dimension n. The finding shows that the nonabelian tensor square of the group is nonabelian and its generalized presentation is constructed.
Keywords: Bieberbach Group, Generalization, Nonabelian Tensor Square, Symmetric Point Group