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The Computation of the Abelianization of All Bieberbach Groups of Dimension Five with Symmetric Point Group of Order Six

Y. T. Tan, R. Masri, N. Mohd Idrus, W. N. F. Wan Mohd Fauzi, N. H. Sarmin, H. I. Mat Hassim


The abelianization of a group is defined as the quotient of the group to its derived subgroup. Bieberbach groups with symmetric point group of order six are torsion free crystallographic groups. The properties of these groups can be explored by computing its abelianization. The aim of this paper is to determine the abelianization of all Bieberbach groups of dimension five with symmetric point group of order six.


Abelianization; Bieberbach group.

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