The Exterior Squares of Some Crystallographic Groups

A crystallographic group is a discrete subgroup g of the set of isometries of euclidean space e^n , where the quotient space e^n/g is compact. a specific type of crystallographic groups is called bieberbach groups. a bieberbach group is defined to be a torsion free crystallographic group. in this paper, the exterior squares of some bieberbach groups with abelian point groups are computed. the exterior square of a group is the factor group of the nonabelian tensor square with the central subgroup of the group.