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ISSN 1079-6762

 

 

The groups of order at most 2000


Authors: Hans Ulrich Besche, Bettina Eick and E. A. O'Brien
Journal: Electron. Res. Announc. Amer. Math. Soc. 7 (2001), 1-4
MSC (2000): Primary 20D10, 20D15; Secondary 20-04
Published electronically: February 12, 2001
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Abstract | References | Similar Articles | Additional Information

Abstract:

We announce the construction up to isomorphism of the $49\,910\,529\,484$ groups of order at most 2000.


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

  • 1. Hans Ulrich Besche, Bettina Eick, and E. A. O'Brien, ``A millennium project: constructing small groups'', Preprint.
  • 2. Hans Ulrich Besche and Bettina Eick, Construction of finite groups, J. Symbolic Comput. 27 (1999), no. 4, 387–404. MR 1681346, 10.1006/jsco.1998.0258
  • 3. Hans Ulrich Besche and Bettina Eick, ``The groups of order $q^n \cdot p$'', Comm. Algebra 2001.
  • 4. Bettina Eick and E. A. O’Brien, Enumerating 𝑝-groups, J. Austral. Math. Soc. Ser. A 67 (1999), no. 2, 191–205. Group theory. MR 1717413
  • 5. The GAP Group, GAP--Groups, Algorithms, and Programming, Version $4.2$, Lehrstuhl D fur Mathematik, RWTH Aachen and School of Mathematical and Computational Sciences, University of St Andrews, 2000.
  • 6. Marshall Hall Jr. and James K. Senior, The groups of order 2ⁿ(𝑛≤6), The Macmillan Co., New York; Collier-Macmillan, Ltd., London, 1964. MR 0168631
  • 7. Graham Higman, Enumerating 𝑝-groups. I. Inequalities, Proc. London Math. Soc. (3) 10 (1960), 24–30. MR 0113948
  • 8. Reinhard Laue, Zur Konstruktion und Klassifikation endlicher auflösbarer Gruppen, Bayreuth. Math. Schr. 9 (1982), ii+304 (German). MR 651224
  • 9. M. F. Newman, Determination of groups of prime-power order, Group theory (Proc. Miniconf., Australian Nat. Univ., Canberra, 1975), Springer, Berlin, 1977, pp. 73–84. Lecture Notes in Math., Vol. 573. MR 0453862
  • 10. John Cannon and Derek Holt (eds.), Computational algebra and number theory, Elsevier Ltd, Oxford, 1997. J. Symbolic Comput. 24 (1997), no. 3-4. MR 1484477
  • 11. Joachim Neubüser, ``Die Untergruppenverbände der Gruppen der Ordnungen $\leq 100$ mit Ausnahme der Ordnungen 64 und 96'',
    Habilitationsschrift, Kiel, 1967.
  • 12. E. A. O’Brien, The 𝑝-group generation algorithm, J. Symbolic Comput. 9 (1990), no. 5-6, 677–698. Computational group theory, Part 1. MR 1075431, 10.1016/S0747-7171(08)80082-X
  • 13. László Pyber, Asymptotic results for permutation groups, Groups and computation (New Brunswick, NJ, 1991) DIMACS Ser. Discrete Math. Theoret. Comput. Sci., vol. 11, Amer. Math. Soc., Providence, RI, 1993, pp. 197–219. MR 1235804
  • 14. Charles C. Sims, Enumerating 𝑝-groups, Proc. London Math. Soc. (3) 15 (1965), 151–166. MR 0169921

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Additional Information

Hans Ulrich Besche
Affiliation: Lehrstuhl D für Mathematik, RWTH Aachen, Templergraben 64, 52062 Aachen, Germany
Email: hbesche@math.rwth-aachen.de

Bettina Eick
Affiliation: Fachbereich Mathematik, Universität Kassel, Heinrich-Plett-Str. 40, 34132 Kassel, Germany
Email: eick@mathematik.uni-kassel.de

E. A. O'Brien
Affiliation: Department of Mathematics, University of Auckland, Private Bag 92019, Auckland, New Zealand
Email: obrien@math.auckland.ac.nz

DOI: http://dx.doi.org/10.1090/S1079-6762-01-00087-7
Keywords: Enumeration, determination, small groups, algorithms
Received by editor(s): May 31, 2000
Published electronically: February 12, 2001
Additional Notes: This work was supported in part by the Marsden Fund of New Zealand via grant #9144/3368248. Eick and O’Brien acknowledge the financial support of the Alexander von Humboldt Foundation, Bonn.
Communicated by: Efim Zelmanov