|
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
Retrieve article in:
PDF
Abstract |
References |
Similar articles |
Additional information
Abstract:
We announce the construction up to isomorphism of the 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
'', Comm. Algebra 2001. - 4.
- Bettina Eick and E. A. O'Brien, ``Enumerating
-groups'', J. Austral. Math. Soc. Ser. A 67 (1999), 191-205. MR 2000h:20033 - 5.
- The GAP Group, GAP--Groups, Algorithms, and Programming, Version
, 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
, Macmillan, New York, 1964. MR 29:5889 - 7.
- Graham Higman, ``Enumerating
-groups. I: Inequalities'', Proc. London Math. Soc. 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
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
-groups'', Proc. London Math. Soc. 15 (1965), 151-166. MR 30:164
Similar Articles:
Retrieve articles in Electronic Research Announcements
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
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
|