On the Generalization of the Nonabelian Tensor Square of a Bieberbach Group with Symmetric Point Group

Abstract

The nonabelian tensor square is a homological functor which can reveal the properties of a group. Meanwhile, a Bieberbach group with symmetric point group of order six is polycyclic. In this paper, by using the method constructed for polycyclic groups, the nonabelian tensor square of the group is computed and generalized up to dimension n. The finding shows that the nonabelian tensor square of the group is nonabelian and its generalized presentation is constructed.