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On integral groups. III. Normalizers


Authors: H. Brown, J. Neubüser and H. Zassenhaus
Journal: Math. Comp. 27 (1973), 167-182
MSC: Primary 20H15
DOI: https://doi.org/10.1090/S0025-5718-1973-0333025-7
MathSciNet review: 0333025
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Abstract: Methods for determining a generating set for the normalizer of a finite group of $ n \times n$ integral matrices, i.e., an n-dimensional crystallographic point group, are discussed. Necessary and sufficient conditions for the finiteness of such a normalizer are derived, and several examples of the application of the methods to cases when the normalizer is infinite are presented.


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DOI: https://doi.org/10.1090/S0025-5718-1973-0333025-7
Keywords: Crystallographic groups, integral matrix groups
Article copyright: © Copyright 1973 American Mathematical Society