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As the Bibliography shows, GAP has been used in a wide variety of areas of mathematics. On this page we first provide some direct links to examples that are intended to give a flavour of the use of GAP. Pointers to some further sources of examples are given below.

  • Analyzing Rubik's Cube with GAP
    An updated GAP 4 version of a GAP 3 example by Martin Schönert, 1993. An almost classical permutation group of small degree is examined with some elementary GAP commands.
  • Two fundamental groups from A. Cavicchioli
    This example demonstrates some methods for the investigation of finitely presented groups using two presentations of fundamental groups due to A. Cavicchioli.
  • Lifting a quotient of type McL of a finitely presented group
    An example by Alexander Hulpke demonstrating how a known (non-solvable) quotient of a finitely presented group can be extended with sovable normal subgroups.
  • Balanced presentations for covering groups of simple groups
    An example that demonstrates how the deficiency of some perfect groups may be determined by a program PGRelFind using GAP together with the ACE package. 2001.
  • Quotients of Grigorchuk's group
    Investigation of some factor groups of a group of automorphisms of a binary tree defined by R. I. Grigorchuk.
  • A solvable subgroup of Fi23
    In this example from the Diploma thesis of Alexander Hulpke a solvable maximal subgroup of Fi23 is constructed using information from the ATLAS.
  • Constructing HS and Co3
    This is a GAP 4 version of the last example in the paper "Construction of Co3. An example of the use of an integrated system for Computational Group Theory", Groups St Andrews 1997 in Bath, by Alexander Hulpke and Steve Linton.
  • A p-Group with Special Properties
    Using a function provided by Bettina Eick a p-group with rather special properties of lower and upper central series, requested in a Forum letter, is constructed and investigated, also using XGAP to depict the lattice of its normal subgroups.

Further Sources of Examples

  • Alexander Hulpke keeps a collection of worked-out solutions of problems raised in the GAP Forum.
  • In the section Applications of the home page for 'The Character Table Library' Thomas Breuer provides a number of examples from character and representation theory.
  • Götz Pfeiffer, in his paper Character Tables of Weyl Groups in GAP, gives a guideline for an implementation in GAP 3.
  • The XGAP manual describes the use of a graphical interface for the investigation of the subgroup structure of some groups aided by the graphical display of parts of the subgroup lattice.
  • The ITC manual describes examples of the interactive use of coset table methods for the investigation of finite fg groups.
  • Some other package manuals also contain rather extensive examples for the use of the respective packages.
  • Further examples of the use of GAP can be found in some discussions kept in the Forum Archive.