The central subgroups of the nonabelian tensor squares of some bieberbach groups with elementary abelian 2-group point group

Abstract

Bieberbach groups are torsion free crystallographic groups. In this paper, our focus is on the Bieberbach groups with elementary abelian 2-group point group, C2 × C2. The central subgroup of the nonabelian tensor square of a group G is generated by gxg for all g in G. The purpose of this paper is to compute the central subgroups of the nonabelian tensor squares of two Bieberbach groups with elementary abelian 2-point group of dimension three.