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An algorithm for the determination of space groups


Author: Harold Brown
Journal: Math. Comp. 23 (1969), 499-514
MSC: Primary 20.60; Secondary 65.00
DOI: https://doi.org/10.1090/S0025-5718-1969-0246975-6
MathSciNet review: 0246975
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Abstract: This semiexpository paper presents in detail a numerical formulation of an algorithm for the determination of all $ n$-dimensional, crystallographic space groups. The implementation of this algorithm on a digital computer is also described.


References [Enhancements On Off] (What's this?)

  • [1] E. Ascher & A. Janner, "Algebraic aspects of crystallography," Helv. Phys. Acta., v. 38, 1965, pp. 551-572. MR 33 #7420. MR 0199271 (33:7420)
  • [2] L. Bieberbach, "Über die Bewegungsgruppen der Euklidischen Räume. I," Math. Ann., v. 70, 1910, pp. 297-336.
  • [3] L. Bieberbach, "Die Gruppen mit endlichem Fundamentalbereich," Math. Ann., v. 72, 1912, pp. 400-412. MR 1511704
  • [4] L. Bieberbach, "Über die Minkowskische Reduktion der positiven quadratischen Formen und die endlichen Gruppen linear ganzzahliger Substitutionen," Nachr. Akad. Wiss. Göttingen, 1912, pp. 207-216.
  • [5] H. Brown, J. Neubüser & H. Zassenhaus, "The 4-dimensional finite unimodular groups." (To appear.)
  • [6] M. Buerger, Elementary Crystallography, Wiley, New York, 1956.
  • [7] H. S. M. Coxeter & W. O. J. Moser, Generators and Relations for Discrete Groups, 2nd ed., Ergebnisse der Math, und ihrer Grenzgebiete, Bd. 14, Springer-Verlag, New York, 1965. MR 30 #4818. MR 0174618 (30:4818)
  • [8] M. Jawson, An Introduction to Mathematical Crystallography, American Elsevier, New York, 1965. MR 0198917 (33:7067)
  • [9] W. Magnus, A. Karrass & D. Solitar, Combinatorial Group Theory: Presentations of Groups in Terms of Generators and Relations, Pure and Appl. Math., vol. 13, Interscience, New York, 1966. MR 34 #7617... MR 0207802 (34:7617)
  • [10] H. Zassenhaus, "Über einen Algorithmus zur Bestimmung der Raumgruppen," Comment. Math. Helv., v. 21, 1948, pp. 117--141. MR 9, 491. MR 0024424 (9:491e)

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1969-0246975-6
Article copyright: © Copyright 1969 American Mathematical Society

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