Publications and Preprints

Alexander Hulpke

-> Paper       -> Theses       -> Software       -> Varia      -> Home

For portability and readability most of the newer files are provided in PDF format.
(You can download the free Acrobat Reader software here.)


Translating MAGMA code to GAP
Computeralgebra Rundbrief 58, 2016
Connected quandles and transitive groups
Joint work with David Stanovsk\'y, Petr Vojt\v{e}chovsk\'y,
Journal of Pure and Applied Algebra, 220 (2016), 735--758 (Official:
Constructing All Composition Series of a Finite Group
Proc. ISSAC 2015, 229--234
Algorithms for arithmetic groups with the congruence subgroup property
Joint work with Alla Detinko and Dane Flannery,
Journal of Algebra 421 (2015), 234--259 (Official:
Software for groups: theory and practice
Mathematical software -- ICMS 2014, 87--91. (Official:
Aristotle's problem
Joint work with Victor Pambuccian,
Beiträge zur Algebra und Geometrie (2014), (official:
Computing Conjugacy Classes of elements in matrix groups
J. Algebra 2013 (official:
Calculation of the Subgroups of a Trivial-Fitting Group
ISSAC 2013
Computing Generators of Groups preserving a Bilinear Form over Residue Class Rings
J.Symb.Comp. 50 (2013), 298-307 (official:
Computing Hall subgroups of finite groups
Joint work with Bettina Eick
LMS J. Comput. Math. 15 (2012), 205–218
The Tits Alternative for Short Generalized Tetrahedron Groups
Joint work with Benjamin Fine, Volkmar große Rebel, Gerhard Rosenberger and Stefanie Schauerte
Revista Scientia, 21 (2011), 1–15
The number of Latin squares of order 11
Joint work with PetteriKaski and Patric R.J. Östergård,, Math.Comp. 80 (2011), 1197-1219
Polytopes derived from sporaic simple groups
Joint work with Michael Hartley,
Contributions to Discrete Mathematics 5:2, 106-118
Normalizer Calculation using automorphisms
Computational Group Theory and the Theory of Groups, Contemp.Math.470 (2008), p.105–109
The Tits Alternative for Spherical Generalized Tetrahedron Groups
Joint work with Benjamin Fine,Volkmar große Rebel and GerhardRosenberger,
Algebra Colloquium, 15:4 (2008) 541–554
All Finite Generalized Tetrahedron Groups
Joint work with Benjamin Fine, Miriam Hahn, Volkmar große Rebel, Gerhard Rosenberger and Martin Scheer,
Algebra Colloquium, 15:4 (2008) 555– 580
On orbifold coverings of genus 2 surfaces
Joint work with Tapani Kuusalo, Marjatta N\"a\"at\"anen and Gerhard Rosenberger.
Revista Scientia 11 (2005), 45-55
Constructing Transitive Permutation Groups
J. Symb. Comp. 39 (2005), 1-30.
Total Ordering on Subgroups and Cosets
Joint work with Steve Linton.
Proc. ISSAC 2003, 156-160
(© Copyright YYYY by ACM, Inc.)
Short Presentations for Three-Dimensional Unitary Groups
Joint work with Ákos Seress.
Journal of Algebra, 245 (2001), 719--729 (CMP 1863898)
Representing subgroups of finitely presented groups by Quotient Subgroups
Experimental Mathematics 10 (2001), no.3, 369-381.
Efficient Simple Groups
Joint work with Colin Campbell, George Havas and Edmund Robertson.
Comm.Alg.,31 (2003), no. 10, 5191--5197 (MR 2003i:20023)
Computing the maximal subgroups of a permutation group I
Joint work with Bettina Eick.
W. Kantor and Á. Seress, editors, Groups and Computation III, pages 155-168. (MR 2002e-20009)
Conjugacy classes in finite permutation groups via homomorphic images
Math.Comp. 69 (2000), 1633-1651. (MR 2001a-20006)
Computing subgroups invariant under a set of automorphisms
J. Symb. Comp. 27 (1999), 415-427. (MR 2000a-20001)
Computing normal subgroups
Proc. ISSAC '98. (CMP 1 805 183) (© Copyright YYYY by ACM, Inc.)
Techniques for the computation of Galois groups
B.H. Matzat, G.-M. Greuel, and G.Hiss, editors, Algorithmic Algebra and Number Theory, pages 65-77. Springer, Heidelberg, 1999. (MR 2000d-12001)
Galois groups through invariant relations
Proc. Groups'97. (MR 2000k-12002)
Construction of Co3. An example of the use of a CGT system
Joint work with Steve Linton.
Proc. Groups'97. (MR 2000k-12002)
On transitive permutation groups
Joint work with John Conway and John McKay.
LMS J. Comput. Math., 1 (1998), 1-8. (MR 99g-20011)
Block systems of a Galois group
Experimental Mathematics 4 (1995), no.1, 1-9. (MR 96k-12007)


Konstruktion transitiver Permutationsgruppen
My PhD Thesis. RWTH Aachen 1996.
Zur Berechnung von Charaktertafeln
My Diploma Thesis. RWTH Aachen 1993.

Software and Documentation

I'm one of the main authors of the computer algebra system GAP

GAP 4.
Link to the GAP web page in St Andrews. From here you can download the system or get more information.
GAP 4 Tutorial
Given at ISSAC 2000.


Suggestion of a format for a library of sporadic groups

1994. (This is probably outdated by now, but as there are references to this, I keep it here)
GAP 3 interface for this library


The documents contained in this directory are included by the contributing authors as a means to ensure timely dissemination of scholarly and technical work only on a non commercial basis. Copyright and all rights therein are maintained by the authors or by other copyright holders, notwithstanding that they have offered there works here electronically. It is understood that all persons copying this information will adhere to the terms and constraints invoked by each author's copyright. These works may not be reposted without the explicit permission of the copyright holder.

Alexander Hulpke (