Formulation of the Nonabelian Tensor Square of a Bieberbach Group
Rohaidah Masri1, Nor Fadzilah Abdul Ladi2, Nor’ashiqin Mohd Idrus3, Nor Haniza Sarmin4
1Rohaidah Masri, Department of Mathematics, Faculty of Science and Mathematics, Universiti Pendidikan Sultan Idris, Tanjung Malim, Perak, Malaysia.
2Nor Fadzilah Abdul Ladi, Department of Mathematics, Faculty of Science and Mathematics, Universiti Pendidikan Sultan Idris, Tanjung Malim, Perak, Malaysia
3Nor’ashiqin Mohd Idrus, Department of Mathematics, Faculty of Science and Mathematics, Universiti Pendidikan Sultan Idris, Tanjung Malim, Perak, Malaysia.
4Nor Haniza Sarmin, Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, UTM, Johor Bahru, Johor, Malaysia.
Manuscript received on 27 June 2019 | Revised Manuscript received on 15 July 2019 | Manuscript Published on 26 July 2019 | PP: 260-263 | Volume-8 Issue-2S2 July 2019 | Retrieval Number: B10460782S219/2019©BEIESP | DOI: 10.35940/ijrte.B1046.0782S219
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© The Authors. Blue Eyes Intelligence Engineering and Sciences Publication (BEIESP). This is an open access article under the CC-BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
Abstract: A Bieberbach set can be categorized as a torsion free crystallographic set. Some properties can be explored from the set such as the property of nonabelian tensor square. The nonabelian tensor square is one type of the homological factors of sets. This paper focused on a Bieberbach set with C2 ×C2 as the point set of lowest dimension three. The purpose of this paper is to determine the generalization of the formula of the nonabelian tensor square of one Bieberbach set with point set C2 × C2of lowest dimension three which is denoted by S2 (3) up to dimensionn. The polycyclic presentation, the abelianization of S2 (3) and the central subgroup of the nonabelian tensor square of S2 (3) are also presented.
Keywords: Bieberbach Set, Nonabelian Tensor Square, Homological Functor.
Scope of the Article: Cryptography and Applied Mathematics