GAP package NQL

The GAP package NQL - Version 0.08

René Hartung

Postal address of the university:
University of Braunschweig
Institute of Computational Mathematics
Pockelsstraße 14
38106 Braunschweig
Germany
Email:
r.hartung [ed] tu-braunschweig.de

Finitely L-presented Groups

A finitely L-presented group is a finitely generated group which might have infinitely many relations. Their relations are given recursively by the action of a finitely generated free monoid of substitutions. Hence these groups can be handled by computer algorithms like those provided by the NQL package.

Some well-known examples of finitely L-presented groups (which are not finitely presentable) are the Grigorchuk group and the Gupta-Sidki group. Both groups arise in the 1980s as famous counter-examples to the General Burnside Problem as they are both finitely generated infinite torsion groups.

Description

Abilities:

The NQL package defines new GAP objects to work with finitely L-presented groups. The main part of the package is a nilpotent quotient algorithm for finitely L-presented groups. This is an algorithm which takes as input a finitely L-presented group G and a positive integer c. It computes a polycyclic presentation for the lower central series quotient G / γc(G).

Requirements:

The package is written for GAP version 4.4. It requires the packages Polycyclic, AutPGrp, and FGA which are loaded automatically when loading the NQL package. Further we suggest to load the ParGap package for using the parallel version of the nilpotent quotient algorithm.

Installation:

The installation follows standard GAP rules. So, the normal way to install the package is to unpack the archive in the `pkg' directory and load the package from within GAP using 'LoadPackage("NQL");'.

Compiling the Manual:

To get the manual and the GAP Help System work you have to compile the documentation of the NQL package. Therefore change into the 'doc' directory of the NQL package and compile the manual via 'make'.

Copyright:

The NQL package is free software; you can redistribute and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your opinion) any later version. The NQL package is distributed in the hope that it will be useful, but without any warranty; without even the implied warranty of merchantability or fitness for a particular purpose. See the GNU General Public License for more details.

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