GAP Modules
This is a list of all accepted modules. It names the original
authors as well as the present maintainers. If no maintainer is
named the module is maintained by the whole of the
GAP Group in the same way as the rest of the
GAP library.
 Permutation Group Pcgs
by Heiko Theissen,
maintained by
Alexander Hulpke, Fort Collins
This code provides the solvable permgroup stabilizer chain and
(modulo) pcgs data structures for permutation groups.
 DixonSchneider Algorithm
by Alexander Hulpke,
maintained by
Alexander Hulpke, Fort Collins
Dixon/Schneider algorithm for ordinary character tables of
finite groups.
 Classes in nonsolvable groups
by Alexander Hulpke,
maintained by
Alexander Hulpke, Fort Collins
Conjugacy classes for nonsolvable groups (homomorphism
principle/subgroups of wreath products).
 Homomorphism search
by Alexander Hulpke,
maintained by
Alexander Hulpke, Fort Collins
Search for Homomorphisms between two groups.
 Subgroup lattice for solvable groups
by Alexander Hulpke,
maintained by
Alexander Hulpke, Fort Collins
(Invariant) subgroups of a solvable group by homomorphism
principle.
 Transitive groups library
by Alexander Hulpke,
maintained by
Alexander Hulpke, Fort Collins
Access to the library of transitive permutation groups of small
degree.
 Cosets and Double Cosets
by Alexander Hulpke,
maintained by
Alexander Hulpke, Fort Collins
Basic functions for cosets and to compute double cosets.
 Factor groups
by Alexander Hulpke,
maintained by
Alexander Hulpke, Fort Collins
(Heuristic) routines to compute faithful permutation
representations of factor groups, in particular for nonsolvable
permutation groups.
 Homomorphisms for finitely presented groups
by Alexander Hulpke,
maintained by
Alexander Hulpke, Fort Collins
Homomorphism functions for finitely presented groups, using
rewriting.
 Primitive groups library
by Heiko Theissen and Colva RoneyDougal
maintained by
Colva RoneyDougal, St Andrews
Access to the library of primitive permutation groups of small
degree.
 Partition Backtrack algorithm
by Heiko Theissen,
maintained by
Alexander Hulpke, Fort Collins
Backtrack algorithm for finding subgroups or elements of
permutation groups.
 1Cohomology and Complements
by Frank Celler and Alexander Hulpke,
maintained by
Alexander Hulpke, Fort Collins
Routines for 1cohomology and complements for solvable normal
subgroups.
 Rational Functions
by Frank Celler and Alexander Hulpke,
maintained by
Alexander Hulpke, Fort Collins
Rational Functions and Polynomials, Arithmetic and
Factorization.
 Subgroup lattice
by Martin Schönert and Alexander Hulpke,
maintained by
Alexander Hulpke, Fort Collins
Cyclic extension algorithm and search for perfect subgroups
Calculation of normal subgroups.
 Group actions
by Heiko Theissen and Alexander Hulpke,
maintained by
Alexander Hulpke, Fort Collins
Methods for orbits, stabilizers, action representatives.
 Finitely presented groups
by Volkmar Felsch, Alexander Hulpke, and
Martin Schönert,
maintained by
Alexander Hulpke, Fort Collins
Methods for subgroups and elements of finitely presented
groups (excludes subgroup presentations and Tietze transformations).
 Subgroup presentations
by Volkmar Felsch,
no official maintainer
Subgroup presentations by rewriting.
 Tietze transformations
by Volkmar Felsch,
no official maintainer
Tietze transformations.
 Stabilizer Chains
by Ákos Seress and Heiko Theissen,
maintained by
Alexander Hulpke, Fort Collins
Routines for stabilizer chains.
 Permutation group homomorphisms
by Ákos Seress and Heiko Theissen,
maintained by
Alexander Hulpke, Fort Collins
Routines for stabilizer chains.
 Random SchreierSims
by Ákos Seress
no official maintainer
Random SchreierSims and verification routine.
 Permutation group composition series
by Ákos Seress
no official maintainer
Composition series for permutation groups, PCore, Radical.
 Multiplier and Schur cover
by Werner Nickel and Alexander Hulpke,
maintained by
Alexander Hulpke, Fort Collins
Calculation of multiplier, Schur Cover epimorphism.
 The Help System
by Frank Lübeck
(replacing the file help.g by Frank Celler),
maintained by
Frank Lübeck, Aachen
Interface between the GAP help system, manual books and viewer.
 Strings and Characters
by Martin Schönert, Frank Celler, Thomas Breuer,
and Frank Lübeck,
maintained by
Frank Lübeck, Aachen
Strings, characters and utilities.
 Classical Groups
by Thomas Breuer, Frank Celler, Stefan Kohl,
Frank Lübeck, and Heiko Theißen,
maintained by
Thomas Breuer, Aachen,
Stefan Kohl, and
Frank Lübeck, Aachen
Classical groups as matrix groups and specialized functions
for them.
 Kernel
by Frank Celler, Steve Linton, Frank Lübeck,
Werner Nickel, and Martin Schönert,
maintained by
Max Horn, Gießen,
Chris Jefferson, St Andrews
Steve Linton, St Andrews,
Frank Lübeck, Aachen, and
Markus Pfeiffer, St Andrews
Interpreter of GAPlanguage, user interface, memory management,
basic data structures and basic operations for them.
 Special Pcgs for finite pc groups
by Bettina Eick,
maintained by
Bettina Eick, Braunschweig.
This module contains an algorithm to determine a special
pcgs for a finite pc group.
 Automorphism groups of finite pc groups
by Bettina Eick,
no official maintainer
This module contains an algorithm to determine the automorphism
group of a finite pc group. The implementation follows the ideas
of Micheal Smith.
 Twocohomology and extensions of finite pc groups
by Bettina Eick,
maintained by
Bettina Eick, Braunschweig.
This module contains methods to compute the second cohomology
group and extensions of finite pc groups.
 Irreducible Modules over finite fields for finite pc
groups
by Bettina Eick,
maintained by
Bettina Eick, Braunschweig.
This module contains Plesken's algorithm to compute the
irreducible representations of a finite pc group over a
finite field.
 Isomorphism testing with random methods
by Hans Ulrich Besche and Bettina Eick,
maintained by
Bettina Eick, Braunschweig.
This module contains an algorithm to test isomorphism of
pc groups using a random method.
 Properties and attributes of finite pc groups
by Frank Celler and Bettina Eick,
no official maintainer
This module contains algorithm to test certain properties
and compute certain attributes of finite pc groups.
 Intersection of subgroups of finite pc groups
by Frank Celler and Bettina Eick,
no official maintainer
This module contains an algorithm to compute the intersection
of subgroups of finite pc groups.
 Finitely presented monoids and semigroups
by Isabel Araujo, Derek Holt, Alexander Hulpke,
Götz Pfeiffer, and Andrew Solomon,
maintained by
James Mitchell, St Andrews
Code for dealing with finitely presented semigroups and
monoids, including the implementation of KnuthBendix
and ToddCoxeter.
 Documentation Utilities
by Frank Celler, Heiko Theissen, Alexander Hulpke,
Willem de Graaf, Steve Linton, Werner Nickel, and Greg Gamble,
maintained by
Greg Gamble, Perth WA
Elements that produce the online text help in GAP, the TeX
produced manuals (.dvi, .ps, .pdf) and HTML manuals, and the
documentation of how these work.
 Binary Relations
by Andrew Solomon and Robert F. Morse,
maintained by
Robert F. Morse, Evansville
This library code provides support for binary relations and
equivalence relations.
 Congruences of magmas, semigroups and monoids
by Andrew Solomon and Robert F. Morse,
maintained by
Robert F. Morse, Evansville
This library code computes congruences for a set with one
binary operator. Faster methods are used when
associativity is known.
 Semigroup relations
by Andrew Solomon, Isabel Araujo, and Robert
F. Morse,
maintained by
Robert F. Morse, Evansville
This library code computes Green's relations of semigroups.
 Transformation semigroups
by Andrew Solomon, Isabel Araujo, and Robert
Arthur,
maintained by
Robert F. Morse, Evansville
This library code implements transformations, and methods
on semigroups represented by them.
 Cyclotomics
by Thomas Breuer
maintained by
Thomas Breuer, Aachen
Cyclotomics and subfields of cyclotomic fields.
 Lie algebras
by Thomas Breuer, Willem de Graaf, Craig Struble,
and Jürgen Wisliceny,
maintained by
Willem de Graaf, Povo (Trento)
Functionality for dealing with Lie algebras and their
representations.
 GAP for MacOS
by Burkhard Höfling,
maintained by
Burkhard Höfling, Braunschweig
This set of files provides the implementation of system dependent
GAP functions and a user interface to run GAP under MacOS.
 Identification of Galois groups
by Alexander Hulpke,
maintained by
Alexander Hulpke, Fort Collins
Functionality for determining the permutation isomorphism type
of a Galois group.
 Characters and Character Degrees of certain solvable
groups
by Hans Ulrich Besche and Thomas Breuer,
maintained by
Thomas Breuer, Aachen
Computation of irreducible character degrees of solvable groups,
using the algorithm of Conlon (see [Con90b]),
and of irreducible characters of (abelian by) supersolvable
groups, using the algorithms of BaumClausen (see [BC94]) and
Conlon (see [Con90a]).
 Possible Permutation Characters
by Thomas Breuer and Götz Pfeiffer,
maintained by
Thomas Breuer, Aachen
Computation of characters that have certain properties of
permutation characters, as is described in [Bre91].
 Possible Class Fusions, Possible Power Maps
by Thomas Breuer,
maintained by
Thomas Breuer, Aachen
Computation of possible class fusions and possible power
maps, based on [Bre91], [Bre99].
 Monomiality Questions
by Thomas Breuer and Erzs'ebet Horv'ath,
maintained by
Thomas Breuer, Aachen
Monomiality of finite (solvable) groups and their characters.
 Structure Descriptions for Finite Groups
by Gábor Horváth, Stefan Kohl, Markus Püschel and
Sebastian Egner,
maintained by
Gábor Horváth, Debrecen and
Stefan Kohl
A method for computing structure descriptions for finite groups.
