GAP

Main Branches

Downloads  Installation  Overview  Data Libraries  Packages  Documentation  Contacts  FAQ  GAP 3 

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.
     
  • Dixon-Schneider 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 Roney-Dougal
    maintained by Colva Roney-Dougal, 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.
     
  • 1-Cohomology and Complements   by Frank Celler and Alexander Hulpke,
    maintained by Alexander Hulpke, Fort Collins

    Routines for 1-cohomology 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 Schreier-Sims   by Ákos Seress
    no official maintainer

    Random Schreier-Sims 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 GAP-language, 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 Knuth-Bendix and Todd-Coxeter.
     
  • 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 on-line 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 Baum-Clausen (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.