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

A finite algorithm for calculating a finite set of generators for the norma lizer 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 algo rithm and is needed for testing equivalence of superspace groups.