The Generalization of the Exterior Square of a Bieberbach Group with Symmetric Point Group

Authors

  • Nor'ashiqin Mohd. Idrus Department of Mathematics, Faculty of Science and Mathematics, Universiti Pendidikan Sultan Idris, Tanjung Malim, Perak
  • Tan Yee Ting Department of Mathematics, Faculty of Science and Mathematics, Universiti Pendidikan Sultan Idris, Tanjung Malim, Perak
  • Rohaidah Masri Department of Mathematics, Faculty of Science and Mathematics, Universiti Pendidikan Sultan Idris, Tanjung Malim, Perak
  • Nor Haniza Sarmin Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Johor
  • Hazzirah Izzati Mat Hassim Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Johor.

DOI:

https://doi.org/10.26713/jims.v8i4.559

Keywords:

Exterior square, Bieberbach group, symmetric point goup

Abstract

The exterior square is a homological functor originated in the homotopy theory, while Bieberbach groups with symmetric point group are torsion free crystallographic groups. In this paper, the generalization of the exterior square of a Bieberbach group with symmetric point group is constructed up to finite dimension.

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References

G. Ellis, On the computation of certain homotopical functors, LMS Journal of Computation and Mathematics 1 (1998), 25-41.

R. Brown and J. L. Loday, Van kampen theorems for diagrams of spaces, Topology 26 (1987), 311-335.

Y. T. Tan, N. Mohd. Idrus, R. Masri, W. N. F. Wan Mohd Fauzi, N. H. Sarmin and H. I. Mat Hassim, The nonabelian exterior square of a Bieberbach group with symmetric point group of order six. (Accepted by Journal of Science and Mathematics)

N. R. Rocco, On a construction related to the nonabelian tensor square of a group, Bol. Soc. Brasil. Mat. (N. S.) 22 (1991), 63-79.

G. Ellis and F. Leonard, Computing Schur multipliers and tensor products of finite groups, Proc. Roy. Irish Acad. 95A(2) (1995), 137-147.

Y. T. Tan, N. Mohd. Idrus, R. Masri, N. H. Sarmin and H. I. Mat Hassim, On the generalization of some homological functors of a Bieberbach group with symmetric point group. (Submitted to Bulletin of the Malaysian Mathematical Sciences Society)

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Published

2016-12-31
CITATION

How to Cite

Idrus, N. M., Ting, T. Y., Masri, R., Sarmin, N. H., & Hassim, H. I. M. (2016). The Generalization of the Exterior Square of a Bieberbach Group with Symmetric Point Group. Journal of Informatics and Mathematical Sciences, 8(4), 295–299. https://doi.org/10.26713/jims.v8i4.559

Issue

Vol. 8 No. 4 (2016)

Section

Research Article

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