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AMS :: Mathematics of Computation

by W. Plesken and W. Hanrath PDF

Math. Comp. 43 (1984), 573-587 Request permission

H. Brown, R. Bülow, J. Neubüser, H. Wondratschek & H. Zassenhaus, Crystallographic Groups of Four-Dimensional Space, Wiley-Interscience, New York, 1978.
• H. Brown, J. Neubüser, and H. Zassenhaus, On integral groups. II. The irreducible case, Numer. Math. 20 (1972/73), 22–31. MR 318335, DOI 10.1007/BF01436640
• John Cannon, A general purpose group theory program, Proceedings of the Second International Conference on the Theory of Groups (Australian Nat. Univ., Canberra, 1973) Lecture Notes in Math., Vol. 372, Springer, Berlin, 1974, pp. 204–217. MR 0354823
• J. D. Jarratt, The decomposition of crystal families, Math. Proc. Cambridge Philos. Soc. 88 (1980), no. 2, 245–263. MR 578269, DOI 10.1017/S0305004100057558
• J. Neubüser, Computing moderately large groups: some methods and applications, Computers in algebra and number theory (Proc. SIAM-AMS Sympos. Appl. Math., New York, 1970) SIAM-AMS Proc., Vol. IV, Amer. Math. Soc., Providence, R.I., 1971, pp. 183–190. MR 0379633
• J. Neubüser, W. Plesken, and H. Wondratschek, An emendatory discursion on defining crystal systems, Match 10 (1981), 77–96. MR 620802
W. Plesken, Beiträge zur Bestimmung der endlichen irreduziblen Untergruppen von $GL(n,{\mathbf {Z}})$, Dissertation, RWTH Aachen, 1974.
• Wilhelm Plesken, The Bravais group and the normalizer of a reducible finite subgroup of $GL(n,\textbf {Z})$, Comm. Algebra 5 (1977), no. 4, 375–396. MR 439948, DOI 10.1080/00927877708822178
• Wilhelm Plesken, On reducible and decomposable representations of orders, J. Reine Angew. Math. 297 (1978), 188–210. MR 466193, DOI 10.1515/crll.1978.297.188
• Wilhelm Plesken, Bravais groups in low dimensions, Match 10 (1981), 97–119 (loose microfiche). MR 620803
• Wilhelm Plesken, Applications of the theory of orders to crystallographic groups, Integral representations and applications (Oberwolfach, 1980) Lecture Notes in Math., vol. 882, Springer, Berlin-New York, 1981, pp. 37–92. MR 646093
• Wilhelm Plesken, Counting with groups and rings, J. Reine Angew. Math. 334 (1982), 40–68. MR 667449, DOI 10.1515/crll.1982.334.40
• Wilhelm Plesken and Michael Pohst, On maximal finite irreducible subgroups of $\textrm {GL}(n, \textbf {Z})$. I. The five and seven dimensional cases, Math. Comp. 31 (1977), no. 138, 536–551. MR 444789, DOI 10.1090/S0025-5718-1977-0444789-X
• Wilhelm Plesken and Michael Pohst, On maximal finite irreducible subgroups of $\textrm {GL}(n,\,\textbf {Z})$. III. The nine-dimensional case, Math. Comp. 34 (1980), no. 149, 245–258. MR 551303, DOI 10.1090/S0025-5718-1980-0551303-7
• S. S. RyÅ¡kov and Z. D. Lomakina, A proof of the theorem on maximal finite groups of integral $5\times 5$ matrices, Trudy Mat. Inst. Steklov. 152 (1980), 204–215, 238 (Russian). Geometry of positive quadratic forms. MR 603825

• Retrieve articles in Mathematics of Computation with MSC: 11H06, 20H15, 52A43
• Retrieve articles in all journals with MSC: 11H06, 20H15, 52A43

• © Copyright 1984 American Mathematical Society
• Journal: Math. Comp. 43 (1984), 573-587
• MSC: Primary 11H06; Secondary 20H15, 52A43
• DOI: https://doi.org/10.1090/S0025-5718-1984-0758205-5
• MathSciNet review: 758205

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