The central subgroup of the nonabelian tensor square of bieberbach group with point group c2 x c2

Masri Rohaidah, A. Ladi N. F., Idrus N. M., Tan Y. T., Sarmin N. H.,

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A Bieberbach group with point group C C 2 2  is a free torsion crystallographic group. A central subgroup of a nonabelian tensor square of a group G, denoted by ( ) G is a normal subgroup generated by generator g g  for all g G and essentially depends on the abelianization of the group. In this paper, the formula of the central subgroup of the nonabelian tensor square of one Bieberbach group with point group C C 2 2  , of lowest dimension 3, denoted by 3S (3) is generalized up to n dimension. The consistent polycyclic presentation, the derived subgroup and the abelianization of group this group of n dimension are first determined. By using these presentations, the central subgroup of the nonabelian tensor square of this group of n dimension is constructed. The findings of this research can be further applied to compute the homological functors of this group.

References

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