UPSI Digital Repository (UDRep)
|
UPSI Digital Repository (UDRep)
|
|
|
| ||||||||||||||||
| Full Text : |
| Bieberbach groups are torsion free crystallographic groups. In this paper, our focus is on the Bieberbach groups with elementary abelian 2-group point group, C2 XC2.The centralsubgroup of the nonabelian tensor square of a group G is generated by g x g for all g in G.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. |
| References |
[1] Brown, R. and Loday, J. L. 1987. Van Kampens Theorems
for Diagrams of Spaces. Topology. 26(3): 311-355.
[2] Masri, R. 2009. The Nonabelian Tensor Squares of Certain Bieberbach Groups with Cyclic Point Group of Order Two. Ph.D. Thesis. Universiti Teknologi Malaysia.
[3] Mohd Idrus, N. 2011. Bieberbach Groups with Finite Point Groups. Ph.D. Thesis. Universiti Teknologi Malaysia.
[4] 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.
[5] 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.
[6] 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.
[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.
[8] Blyth, R. D. and Morse, R. F. 2009. Computing the
Nonabelian Tensor Squares of Polycyclic Groups. Journal
of Algebra. 321: 2139-2148.
[9] 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.
[10] 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.
[11] 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.
[12] Zomorodian, A. J. 2005. Topology for Computing. New
York: Cambridge University Press.
[13] Gallian, J. A. 2010. Contemporary Abstract Algebra. 7th ed. USA: Cegage LEARNING.
[14] Brown, R., Johnson, D. L. and Robertson, E. F. 1987. Some Computations of Nonabelian Tensor Products of Groups. Journal of Algebra. 111: 177-202.
[15] Magidin,A.and Morse, R. F. 2010. Certain Homological Functors. Contemporary Mathematics.511:127-166. |
| This material may be protected under Copyright Act which governs the making of photocopies or reproductions of copyrighted materials. You may use the digitized material for private study, scholarship, or research. |