Remote Access Electronic Research Announcements

Electronic Research Announcements

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
MathSciNet review: 1826989
Full-text PDF Free Access

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?)

    BescheEickOBrien00 Hans Ulrich Besche, Bettina Eick, and E. A. O’Brien, “A millennium project: constructing small groups”, Preprint.
  • Hans Ulrich Besche and Bettina Eick, Construction of finite groups, J. Symbolic Comput. 27 (1999), no. 4, 387–404. MR 1681346, DOI
  • BescheEick00 Hans Ulrich Besche and Bettina Eick, “The groups of order $q^n \cdot p$”, Comm. Algebra 2001.
  • 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
  • GAP The GAP Group, GAP—Groups, Algorithms, and Programming, Version $4.2$, Lehrstuhl D für Mathematik, RWTH Aachen and School of Mathematical and Computational Sciences, University of St Andrews, 2000.
  • Marshall Hall Jr. and James K. Senior, The groups of order $2^{n}\,(n\leq 6)$, The Macmillan Co., New York; Collier-Macmillan, Ltd., London, 1964. MR 0168631
  • Graham Higman, Enumerating $p$-groups. I. Inequalities, Proc. London Math. Soc. (3) 10 (1960), 24–30. MR 113948, DOI
  • Reinhard Laue, Zur Konstruktion und Klassifikation endlicher auflösbarer Gruppen, Bayreuth. Math. Schr. 9 (1982), ii+304 (German). MR 651224
  • 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
  • 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
  • Neubuser67 Joachim Neubüser, “Die Untergruppenverbände der Gruppen der Ordnungen $\leq 100$ mit Ausnahme der Ordnungen 64 und 96”, Habilitationsschrift, Kiel, 1967.
  • 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, DOI
  • 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
  • Charles C. Sims, Enumerating $p$-groups, Proc. London Math. Soc. (3) 15 (1965), 151–166. MR 169921, DOI

Similar Articles

Retrieve articles in Electronic Research Announcements of the American Mathematical Society with MSC (2000): 20D10, 20D15, 20-04

Retrieve articles in all journals with MSC (2000): 20D10, 20D15, 20-04

Additional Information

Hans Ulrich Besche
Affiliation: Lehrstuhl D für Mathematik, RWTH Aachen, Templergraben 64, 52062 Aachen, Germany

Bettina Eick
Affiliation: Fachbereich Mathematik, Universität Kassel, Heinrich-Plett-Str. 40, 34132 Kassel, Germany
MR Author ID: 614875

E. A. O’Brien
Affiliation: Department of Mathematics, University of Auckland, Private Bag 92019, Auckland, New Zealand
MR Author ID: 251889

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
Article copyright: © Copyright 2001 American Mathematical Society