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We assign names and new generators to the transitive groups of degree up to 15, reflecting their structure.

- Alexander Hulpke
- J. Symb. Comput.
- 2005

This paper presents a new algorithm to classify all transitive subgroups of the symmetric group up to conjugacy. It has been used to determine the transitive groups of degree up to 30.

- Alexander Hulpke
- Math. Comput.
- 2000

The lifting of results from factor groups to the full group is a standard technique for solvable groups. This paper shows how to utilize this approach in the case of non-solvable normal subgroups to compute the conjugacy classes of a finite group.

We give a presentation of length O ( log2 |G| ) for the groups G∼= PSU3(q). This result has applications in recent algorithms to compute the structure of permutation groups and matrix groups.

- Alexander Hulpke
- Experimental Mathematics
- 1995

Supported by the Graduiertenkolleg \Analyse und Konstruktion in der Mathematik".

We prove that the simple group L3(5) which has order 372000 is efficient by providing an efficient presentation for it. This leaves one simple group with order less than one million, S4(4) which has order 979200, whose efficiency or otherwise remains to be determined.

- Alexander Hulpke, Steve Linton
- ISSAC
- 2003

We show how to compute efficiently a lexicographic ordering for subgroups and cosets of permutation groups and, more generally, of finite groups with a faithful permutation representation.

- Alexander Hulpke
- 2013

This article describes a setup that – given a composition tree – provides functionality for calculation in finite matrix groups using the Trivial-Fitting approach that has been used successfully for permutation groups. It treats the composition tree as a black-box object. It thus is applicable to other classes of groups for which a composition tree can be… (More)

- Alexander Hulpke
- ISSAC
- 1998

This note presents a new algorithm for the computation of the set of normal subgroups of a finite group. It is based on lifting via homomorphic images.

- Alexander Hulpke
- J. Symb. Comput.
- 1999

When examining the structure of a finite group G, a typical question is the determination of the conjugacy classes of subgroups. For this problem a well-known algorithm – the cyclic extension method (Neubüser 1960, Mnich 1992) – has been in use for over 30 years. For practical purposes this algorithm is limited to groups of size a few thousand. If the… (More)