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Exploration of a group's properties is vital for better understanding about the group.  Amongst other properties, the homological invariants including the nonabelian tensor square of a group can be explicated by showing that the group is polycyclic.  In this paper, the polycyclic presentations of certain crystallographic groups with quaternion point group of order eight are shown to be consistent; which implies that these groups are polycyclic.

Polycyclic transformations of crystallographic groups with quaternion point group of order eight