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 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.
Zeiner
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Institute for Theoretical Physics, University of Nijmegen, Toernooiveld, 6525 ED Nijmegen, The Netherlands. zeiner@sci.kun.nl
Janssen
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