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On integral groups

I. The reducible case

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Summary

An algorithm for the determination of all integral classes of reducible integral matrix groups of given dimension from those of lower dimension is described. For dimensionn=4 there are 567 such classes.

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References

  1. Brown, H.: An algorithm for the determination of space groups. Math. Comp.23, 499–514 (1969).

    Google Scholar 

  2. Bülow, R., Neubüser, J.: On some applications of group-theoretical programmes to the derivation of the crystal classes ofR 4. Computational problems in abstract algebra, p. 131–135. Oxford: Pergamon Press 1969.

    Google Scholar 

  3. Burckhardt, J. J.: Die Bewegungsgruppen der Kristallographie. Basel: Birkhäuser 1947.

    Google Scholar 

  4. Curtis, C. W., Reiner, J.: Representation theory of finite groups and associative algebras. New York: Interscience 1962.

    Google Scholar 

  5. Dade, E. C.: The maximal finite groups of 4×4 matrices. Illinois J. Math.9, 99–122 (1965).

    Google Scholar 

  6. Diederichsen, F. E.: Über die Ausreduktion ganzzahliger Gruppendarstellungen bei arithmetischer Äquivalenz. Abh. Hamb.13, 357–412 (1940).

    Google Scholar 

  7. Hurley, A. C.: Finite rotation groups and crystal classes in 4-dimensions. Proc. Camb. Phil. Soc.47, 650–661 (1951).

    Google Scholar 

  8. Hurley, A. C., Neubüser, J., Wondratschek, H.: Crystal classes of four-dimensional spaceR 4. Acta Cryst.22, 605 (1967).

    Google Scholar 

  9. Siegel, C. L.: Discontinuous groups. Annals of Math. (2)44, 674–689 (1943).

    Google Scholar 

  10. Zassenhaus, H.: Neuer Beweis für die Endlichkeit der Klassenzahl bei unimodularer Äquivalenz endlicher ganzzahliger Substitutionsgruppen. Abh. Hamh.11, 276–288 (1935).

    Google Scholar 

  11. Zassenhaus, H.: Über einen Algorithmus zur Bestimmung der Raumgruppen. Comm. Helv. Math.21, 117–141 (1948).

    Google Scholar 

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Brown, H., Neubüser, J. & Zassenhaus, H. On integral groups. Numer. Math. 19, 386–399 (1972). https://doi.org/10.1007/BF01404921

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