The Central Subgroup of the Nonabelian Tensor Square of the Second Bieberbach Group with Dihedral Point Group

Abstract

The properties of a group can be explored by computing the homological functors of the group. One of the homological functors of a group is the nabla, which is the central subgroup of the nonabelian tensor square. In this study, the nabla of the second Bieberbach group of dimension five with dihedral point group of order eight is computed. The abelianization of the group is first determined in order to compute its nabla.