Enumerations and Classifications
Bettina Eick
The classification of groups of `small' order is another of my main research projects.
One milestone in this project was the classification of all groups of order at most
2000 (except 1024). The result is available in the well-known Small Groups Library.
In recent years, the classification of groups of order at most 20.000 (with few
exceptions) has been an interesting project.
The enumeration of groups of certain types of orders is a highly interesting more
recent research project. This includes questions whose solution is PORC (polynomial
on residue classes) as initiated by Graham Higman.
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Small Groups and Group Classifications
- Constructing groups of 'small' order: Recent results
and open problems. With M. Horn and A. Hulpke. In Proceedings:
Algorithmic and experimental methods in algebra, geometry, and number theory.
Springer (ISBN 978-3-319-70565-1 and 978-3-319-70566-8), 199 -- 211 (2017).
- The construction of finite solvable groups revised.
With M. Horn. J. Algebra 408, 166 -- 182 (2014).
- On the groups of cube-free order.
With Heiko Dietrich. J. Algebra 292, 122 - 137 (2005)
- A millennium project: constructing small
groups. With Hans Ulrich Besche and E. A. O'Brien.
International Journal of Algebra and Computation 12, 623 - 644 (2002)
- The groups of order at most 2000.
With Hans Ulrich Besche and E. A. O'Brien.
Electronic Research Announcemen Amer. Math. Soc. 7, 1-4 (2001)
- The groups of order q^n * p. With Hans Ulrich Besche.
Comm. Alg. 29(4), 1759 - 1772 (2001)
- Enumerating p-groups. With E. A. O'Brien.
J. Austral. Math. Soc. (Series A) 67, 191 - 205 (1999)
- Construction of finite groups.
With Hans Ulrich Besche.
J. Symb. Comput. 27 (4), 387 - 404 (1999)
- The groups of order at most 1000 except 512 and 768.
With Hans Ulrich Besche. J. Symb. Comput. 27 (4), 405 - 413 (1999)
- The groups of order 512. With E. A. O'Brien.
Proceedings "Abschlusstagung des DFG Schwerpunktes Algorithmische
Algebra und Zahlentheorie" 1997, B.H. Matzat, G.-M. Greuel and
G. Hiss, eds, Springer 379 - 380 (1998)
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