Authors:Rohaidah Masri,Nor Fadzilah Abdul Ladi,Nor’ashiqin Mohd Idrus,Tan Yee Ting,Nor Haniza Sarmin,
Keywords:Bieberbach Group, Polycyclic Groups,Nonabelian Tensor Square,
AbstractA Bieberbach group is a crystallographic group. This group is an extension of a finite point group and a free abelian group of finite rank. In this paper, a Bieberbach group with point group 2 2 C C of dimension three is chosen where its polycyclic presentation is shown to be consistent. The nonabelian tensor square of group is a specialization of more general of the nonabelian tensor product of group. The nonabelian tensor square of group is one of the homological functors which can reveal the properties of the groups. Also, the nonabelian tensor squares are one of the important elements on computing homological functors of groups. The main objective of this paper is to compute the nonabelian tensor square of a Bieberbach group with point group 2 2 C C of dimension three by using the computational method for polycyclic groups. The finding showed that the nonabelian tensor square of the group is abelian and be presented in terms of its generators. The findings of this research can be used to compute the other homological functors of this group.
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