The GAP 4 package `Polycyclic'
==============================
Introduction
------------
This is the package `Polycyclic' written for GAP 4. It provides a
basis for working with polycyclic groups defined by polycyclic
presentations.
To have the full functionality of the package available you need at
least GAP version 4.5 and the GAP 4 package Alnuth and its dependencies
must be installed.
The features of this package include
- creating a polycyclic group from a polycyclic presentation
- arithmetic in a polycyclic group
- computation with subgroups and factor groups of a polycyclic
group
- computation of standard subgroup series such as the derived
series, the lower central series
- computation of the first and second cohomology
- computation of group extensions
- computation of normalizers and centralizers
- solutions to the conjugacy problems for elements and subgroups
- computation of torsion and various finite subgroups
- computation of various subgroups of finite index
- computation of the Schur multiplicator, the non-abelian
exterior square and the non-abelian tenor square
There is a manual in the subdirectory 'doc' written in plain TeX which
describes the available functions in detail.
If you have used `Polycyclic', please let us know by sending an email
to one (or both) of us. If you have found important features missing
or if there is a bug, we would appreciate it very much if you send us
an email.
Bettina Eick <beick@tu-bs.de>
Max Horn <max.horn@uni-siegen.de>
You can also reach us by sending an email to the general GAP email
address for problems with GAP:
support@gap-system.org
Contents
--------
With this version you should have obtained the following files and
directories:
README this file
init.g the file that initializes this package
read.g the file that reads in the package
PackageInfo.g the file for the new package loading mechanism
doc the manual
gap the GAP code, it contains
action actions of polycyclic groups and orbit-stabilizer
basic basic stuff for pcp groups
cohom cohomology for pcp groups
exam examples of pcp groups
matrep matrix representations for pcp groups
matrix basic stuff for matrices and lattices
pcpgrp higher level functions for pcp groups
Installation
------------
Make sure that the GAP 4 package Alnuth is installed to have the full
range of methods available in polycyclic.
There are two ways of installing the package. If you have permission
to add files to the installation directory of GAP 4 on your system,
you may install polycyclic in the pkg subdirectory of the GAP
installation tree. If you do not, you can also install polycyclic in
a directory where you have write permissions. For general advice, see
also the GAP 4 manual about the installation of GAP packages.
-- Installation in the GAP 4 pkg subdirectory on a Unix system.
We assume that the archive file polycyclic.tar.gz or
polycyclic.tar is present in pkg and that the current directory is
pkg. All that needs to be done is to unpack the archive.
sh > tar xzf polycyclic.tar.gz
The tar-command has unpacked the code into a directory called
'polycyclic' in the current directory. You can check if GAP
recognizes the polycyclic package by starting GAP and doing the
following:
sh > gap4
[... startup messages ...]
gap> LoadPackage("polycyclic");
true
gap>
-- Installation in a private directory
Let's say you would like to install polycyclic in a directory
called mygap. Create a subdirectory 'pkg' in mygap and move the
polycyclic archive into that subdirectory.
sh > cd mygap
sh > mkdir pkg
sh > mv polycyclic.tar.gz pkg
sh > tar xzf polycyclic.tar
The tar-command has unpacked the code into a directory called
'polycyclic' in the current directory. You can check if GAP
recognizes the polycyclic package by starting GAP and doing the
following. GAP needs to be told that it should scan the directory
mygap/pkg for GAP packages. This is achieved by calling gap with
the option -l. Note the semicolon and the single quotes.
sh > gap4 -l ';mygap/'
[... startup messages ...]
gap> LoadPackage("polycyclic");
true
gap>