The Central Subgroup of the Nonabelian Tensor Square of the Second Bieberbach Group with Dihedral Point Group

  • Wan Nor Farhana Wan Mohd Fauzi
  • Nor’ashiqin Mohd Idrus
  • Rohaidah Masri
  • Tan Yee Ting
  • Nor Haniza Sarmin
Keywords: homological functors, nabla, abelianization, Bieberbach group

Abstract

The properties of a group can be explored by computing the homological functors of the group. One of the homological functors of a group is the nabla, which is the central subgroup of the nonabelian tensor square. In this study, the nabla of the second Bieberbach group of dimension five with dihedral point group of order eight is computed. The abelianization of the group is first determined in order to compute its nabla.

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Author Biographies

Wan Nor Farhana Wan Mohd Fauzi

Department of Mathematics, Faculty of Science and Mathematics, Universiti Pendidikan Sultan Idris, 35900 Tanjung Malim, Perak, Malaysia

Nor’ashiqin Mohd Idrus

Department of Mathematics, Faculty of Science and Mathematics, Universiti Pendidikan Sultan Idris, 35900 Tanjung Malim, Perak, Malaysia

Rohaidah Masri

Department of Mathematics, Faculty of Science and Mathematics, Universiti Pendidikan Sultan Idris, 35900 Tanjung Malim, Perak, Malaysia

Tan Yee Ting

Department of Mathematics, Faculty of Science and Mathematics, Universiti Pendidikan Sultan Idris, 35900 Tanjung Malim, Perak, Malaysia.

Nor Haniza Sarmin

Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 Johor Bahru, Johor, Malaysia

Published
2015-06-01
How to Cite
Wan Mohd Fauzi, W. N. F., Mohd Idrus, N., Masri, R., Yee Ting, T., & Sarmin, N. H. (2015). The Central Subgroup of the Nonabelian Tensor Square of the Second Bieberbach Group with Dihedral Point Group. Journal of Science and Mathematics Letters, 3, 40-49. Retrieved from https://ejournal.upsi.edu.my/index.php/JSML/article/view/368