A Homological Invariant of a Bieberbach Group with Dihedral Extension

Authors

  • Siti Afiqah Mohammad Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Johor Malaysia
  • Nor Haniza Sarmin Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Johor Malaysia
  • Nor Muhainiah Mohd Ali, Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Johor Malaysia
  • Hazzirah Izzati Mat Hassim Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Johor Malaysia

DOI:

https://doi.org/10.11113/jt.v71.3844

Keywords:

Bieberbach group, homological invariant, dihedral extension

Abstract

A Bieberbach group is a crystallographic group which is an extension of a free abelian group of finite rank by a finite extension. Meanwhile, research on homological invariants has been on interest of many authors since it is related to the study of the properties of the crystal using mathematical approach. One of the homological invariants is the exterior square. In this paper, the exterior square of a Bieberbach group of dimension four with dihedral extension is computed theoretically.

References

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Published

2014-12-30

Issue

Vol. 71 No. 5: ​Special Issue on Fifth International Graduate Conference on Engineering, Science & Humanities

Section

Science and Engineering

License

Copyright of articles that appear in Jurnal Teknologi belongs exclusively to Penerbit Universiti Teknologi Malaysia (Penerbit UTM Press). This copyright covers the rights to reproduce the article, including reprints, electronic reproductions, or any other reproductions of similar nature.

How to Cite

A Homological Invariant of a Bieberbach Group with Dihedral Extension. (2014). Jurnal Teknologi (Sciences & Engineering), 71(5). https://doi.org/10.11113/jt.v71.3844