# THE CENTRAL SUBGROUPS OF THE NONABELIAN TENSOR SQUARES OF SOME BIEBERBACH GROUPS WITH ELEMENTARY ABELIAN 2-GROUP POINT GROUP

## DOI:

https://doi.org/10.11113/jt.v79.10677## Keywords:

Group theory, Bieberbach group, central subgroup, nonabelian tensor square, elementary abelian group## Abstract

Bieberbach groups are torsion free crystallographic groups. In this paper, our focus is on the Bieberbach groups with elementary abelian 2-group point group, Â The central subgroup of the nonabelian tensor square of a group Â is generated by Â for all Â in Â The purpose of this paper is to compute the central subgroups of the nonabelian tensor squares of two Bieberbach groups with elementary abelian 2-point group of dimension three.Â

## References

Brown, R. and Loday, J. L. 1987. Van Kampens Theorems for Diagrams of Spaces. Topology. 26(3): 311-355.

Masri, R. 2009. The Nonabelian Tensor Squares of Certain Bieberbach Groups with Cyclic Point Group of Order Two. Ph.D. Thesis. Universiti Teknologi Malaysia.

Mohd Idrus, N. 2011. Bieberbach Groups with Finite Point Groups. Ph.D. Thesis. Universiti Teknologi Malaysia.

Wan Mohd Fauzi, W. N. F., Mohd Idrus, N., Masri, R., Tan, Y. T. and Sarmin, N. H. 2015. The Central Subgroup of the Nonabelian Tensor Square of the Second Bieberbach Group with Dihedral Point Group. J. Sci. Math. Lett. 3: 40-49.

Tan, Y. T., Masri, R., Mohd Idrus, N., Wan Mohd Fauzi, W. N. F., Sarmin, N. H. and Mat Hassim, H. I. 2015. The Central Subgroup of the Nonabelian Tensor Square of Bieberbach Group of Dimension Six with Symmetric Point Group of Order Six. Int. J. Appl. Math. Stat. 53(4): 98-103.

Mohammad, S. A., Sarmin, N. H. and Mat Hassim, H. I. 2016. The Central Subgroup of the Nonabelian Tensor Square of a Torsion Free Space Group. AIP Conference Proceedings. 1750: 1-7.

Abdul Ladi, N. F., Masri, R., Mohd Idrus, N. and Tan, Y. T. 2016. On The Generalization of The Abelianizations of Two Families of Bieberbach Groups with Elementary Abelian 2-group Pint Group. Proceeding of the 6th International Graduate Conference on Engineering, Science and Humanities. 393-395. ISBN: 978-967-0194-67-7.

Blyth, R. D. and Morse, R. F. 2009. Computing the Nonabelian Tensor Squares of Polycyclic Groups. Journal of Algebra. 321: 2139-2148.

Rocco, N. R. 1991. On a Construction Related to The Nonabelian Tensor Square of a Group. Bol. Soc. Brasil. Mat. (N.S.). 22(1): 63-79.

Blyth,R. D., Fumagalli, F. and Morigi, M. 2010. Some Structural Results on Non-Abelian Tensor Square of Groups. Journal of Group Theory. 13: 83-94.

Blyth, R. D., Moravec, P. and Morse R. F. 2008. On the Nonabelian Tensor Squares of Free Nilpotent Groups of Finite Rank. Contemporary Mathematics. 470: 27-44.

Zomorodian, A. J. 2005. Topology for Computing. New York: Cambridge University Press.

Gallian, J. A. 2010. Contemporary Abstract Algebra. 7th ed. USA: Cegage LEARNING.

Brown, R., Johnson, D. L. and Robertson, E. F. 1987. Some Computations of Nonabelian Tensor Products of Groups. Journal of Algebra. 111: 177-202.

Magidin, A. and Morse, R. F. 2010. Certain Homological Functors. Contemporary Mathematics. 511: 127-166.

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*Jurnal Teknologi*,

*79*(7). https://doi.org/10.11113/jt.v79.10677