Abelianization of space groups.
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.
Ratcliffe
John G
JG
Department of Mathematics, Vanderbilt University, Nashville, TN 37240, USA. j.g.ratcliffe@vanderbilt.edu
Tschantz
Steven T
ST