title: Abelianization of space groups.
abstract: The abelianization of a group is its commutator quotient group. In this paper, we provide tables of the abelianizations of all the n-dimensional space groups for n = 1, 2, 3. We prove that the exponent of the torsion subgroup of the abelianization of an arbitrary n-dimensional space group Gamma divides the order of the point group of Gamma.
authors.affiliation: Department of Mathematics, Vanderbilt University, Nashville, TN 37240, USA. j.g.ratcliffe@vanderbilt.edu
authors.forename: John G
authors.initials: JG
authors.lastname: Ratcliffe
authors.forename: Steven T
authors.initials: ST
authors.lastname: Tschantz