The main objective of this research is to compute the nonabelian tensor squares of some Bieberbach groups with elementary abelian 2-groups point groups, C2×C2 for both abelian and nonabelian cases. This is qualitative research where the computational method for polycyclic groups is used to determine the nonabelian tensor squares of four Bieberbach groups with point group C2 × C2. The findings show that the structures of the nonabelian tensor squares of some of these groups for both abelian and nonabelian cases are found split while some are found non-split. The formulas of the abelian cases of the nonabelian tensor squares of the groups lead to the construction of the formulations of the nonabelian tensor squares of arbitrary dimension. Furthermore, for the nonabelian cases, the presentations of the nonabelian tensor squares of the other two groups are given and it was shown that the nonabelian tensor squares can be written as a direct product with the nonabelian exterior square as o.....

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Bieberbach groups are crystallographic groups. By computing the central subgroup of the nonabelian tensor square of a group, the properties of the group can be determined. In this paper, the central subgroup of the nonabelian tensor square of one Bieberbach group of dimension three with point group C2 × C2 is computed. In order to compute the (S3 (3)), the derived subgroup and the abelianization of the group are first constructed...

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