Notes on the normalizer of a finite subgroup of GL(n,d,Z) in GL(n,d,Z)

Acta Crystallogr A. 2001 May;57(Pt 3):256-63. doi: 10.1107/s0108767300017347. Epub 2001 May 1.

Abstract

A finite algorithm for calculating a finite set of generators for the normalizer of a finite subgroup G of GL(n,d,Z) in GL(n,d,Z) is presented. It is based on an algorithm for the normalizer of a finite subgroup G in GL(n,Z), which has been developed recently by Opgenorth. The normalizer of G in GL(n,d,Z) plays a role for superspace groups analogous to the role that the normalizer of G in GL(n,Z) plays for n-dimensional space groups. It is important for calculating superspace groups with the Zassenhaus algorithm and is needed for testing equivalence of superspace groups.