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The groups of order at most 2000

Author(s): Hans Ulrich Besche; Bettina Eick; E. A. O'Brien
Journal: Electron. Res. Announc. Amer. Math. Soc. 7 (2001), 1-4.
MSC (2000): Primary 20D10, 20D15; Secondary 20-04
Posted: February 12, 2001
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Abstract:

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


References:

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), 387-404. MR 2000c:20001
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), 191-205. MR 2000h:20033
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 $2^n$ $(n \leq 6)$,
Macmillan, New York, 1964. MR 29:5889
7.
Graham Higman, ``Enumerating $p$-groups. I: Inequalities'', Proc. London Math. Soc. $(3)$ 10 (1960), 24-30. MR 22:4779
8.
Reinhard Laue, Zur Konstruktion und Klassifikation endlicher auflösbarer Gruppen, Bayreuth. Math. Schr. no. 9 (1982). MR 84e:20018
9.
M. F. Newman, ``Determination of groups of prime-power order'', Group Theory, Lecture Notes in Math. 573 (Canberra, 1975), pp. 73-84, Springer-Verlag, Berlin, Heidelberg, New York, 1977. MR 56:12115
10.
Wieb Bosma, John Cannon, and Catherine Playoust, ``The MAGMA Algebra System I: The User Language'', J. Symbolic Comput. 24 (1997), 235-265. MR 98f:68006
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), 677-698. MR 91j:20050
13.
László Pyber, ``Asymptotic results for permutation groups'', Amer. Math. Soc. DIMACS Series, 11 (DIMACS, 1991), 1993, pp. 197-219. MR 94g:20003
14.
Charles C. Sims, ``Enumerating $p$-groups'', Proc. London Math. Soc. $(3)$ 15 (1965), 151-166. MR 30:164

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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: 10.1090/S1079-6762-01-00087-7
PII: S 1079-6762(01)00087-7
Keywords: Enumeration, determination, small groups, algorithms
Received by editor(s): May 31, 2000
Posted: 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


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