The Schur multipliers of certain Bieberbach groups with abelian point groups

Abstract

The Schur multiplier of a group G is the kernel of a homomorphism κ′ from the exterior square of the group, G ∧ G to its commutator subgroup, G′ defined by κ′(g ∧ h) = [g,h] for g,h ∈ G. In this research, the Schur multipliers are computed for certain Bieberbach groups with abelian point groups. A Bieberbach group is a torsion free crystallographic group. It is an extension of a free abelian group L of finite rank by a finite group P. Here, L is known as the lattice group while P is the point group of the Bieberbach group.