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

Formulation of the Nonabelian Tensor Square of a Bieberbach Group

“…Masri [6] has started the study of the nonabelian tensor squares of Bieberbach sets with certain cyclic spot group in 2009 and focused on Bieberbach sets with cyclic point set of order two. Next, the other studies which are related to the determination of the formula of the nonabelian tensor squares of other Bieberbach sets with different spot groups have also been done by other researchers such as the dihedral set ( [7], [8]), the cyclic set of order three and five [9], the symmetric point set ([10, [11]) and the elementary abelian 2-set point group [12]. The abelian cases for the nonabelian tensor squares of Bieberbach sets can be found in [6] and these findings lead to the generalization of the formula of nonabelian tensor squares of the sets up to dimension n. Basedon the generalizations in [6], the homological functors of the Bieberbach set such as the schur multiplier, the nonabelian exterior squares can be computed up to dimension n in [9].…”