The nonabelian tensor square of a bieberbach group with elementary Abelian 2-group point group

Abstract

A Bieberbach group is a torsion free crystallographic. In this paper, one Bieberbach group with elementary abelian 2-group point group of the lowest dimension three is considered and its group presentation can be shown to be consistent polycyclic presentation. The main objective of this paper is to compute the nonabelian tensor square of one Bieberbach group with elementary abelian 2-group point group of dimension three by using the computational method of the nonabelian tensor square for polycyclic groups. The finding of the computation showed that the nonabelian tensor square of the group is abelian and the formula of the nonabelian tensor square of the Bieberbach group with elementary abelian 2-group of dimension 3, S₁(3) , can be extended in constructing the generalization of the formula of the nonabelian tensor square of the group up to dimension n.

Keywords: Bieberbach group; polycyclic groups; nonabelian tensor square.