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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 <firstname.lastname@example.org> Max Horn <email@example.com> You can also reach us by sending an email to the general GAP email address for problems with GAP: firstname.lastname@example.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 htm the manual as web pages, start with the page htm/chapters.htm 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 etc developers' stuff 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 > gunzip polycyclic.tar.gz # for the gzipped tar-archive # skip if you have the .tar version sh > tar xf 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: 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 > gunzip polycyclic.tar.gz # for the gzipped tar-archive # skip if you have the .tar version sh > tar xf 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>