GPL, the Group Presentations Library

• The Group Presentations Library.
• 1 Presentations of Sporadic Groups
  • 1.1 GroupRecordGPL
  • 1.2 GroupPresentationGPL
  • 1.3 InitializeGroupPresentationGPL
  • 1.4 GroupPresentationsGPL
  • 1.5 AvailableGroupPresentationsGPL
  • 1.6 SubgroupGPL
  • 1.7 AvailableSubgroupsGPL
  • 1.8 AvailableMaximalSubgroupsGPL
• 2 Finitely Presented Groups Via Strings
  • 2.1 Coxeter graphs
  • 2.2 FpGroupViaStrings
  • 2.3 SubgroupViaStrings
  • 2.4 StringPresentation
  • 2.5 CoxeterStringPresentation
• References

The Group Presentations Library file

1. contains 27 presentations of sporadic groups.
2. contains words generating several subgroups in these presentations.
3. gives a general setup for storing presentations and representations.
4. enables its users to build finitely presented groups via strings and vice versa.

Presentations for all sporadic simple groups from the Mathieu group M11 up to the Higman-Sims group and their automorphism groups are present. In each of these eleven presentations, words are given for every maximal subgroup, up to the action of the automorhism group. Several presentations and words are available for other sporadic groups.

The GPL distribution contains of two files:

gpl.g

the library and functions in GAP format

gpl.ps.gz

documentation in compressed postscript format

These files are also available from GAP's Deposited Contributions site in

• St. Andrews, United Kingdom
• Northeastern University, USA
• Aachen, Germany
• ANU, Australia

Please send bugs and comments to r.c.lindenbergh@geo.tudelft.nl