Computation with polycyclic groups
Version 2.16
Released 2020-07-25
This project is maintained by Bettina Eick, Max Horn
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
which describes the
available functions in detail.
If you have used Polycyclic
, and found important features missing
or if there is a bug, we would appreciate it very much if you could
report this via https://github.com/gap-packages/polycyclic/issues,
or by sending us an email.
With this version you should have obtained the following files and directories:
README
: this fileinit.g
: the file that initializes this packageread.g
: the file that reads in the packagePackageInfo.g
: the file for the new package loading mechanismdoc
: directory containing the manualgap
: directory containing the GAP code, it contains:
action
: actions of polycyclic groups and orbit-stabilizerbasic
: basic stuff for pcp groupscohom
: cohomology for pcp groupsexam
: examples of pcp groupsmatrep
: matrix representations for pcp groupsmatrix
: basic stuff for matrices and latticespcpgrp
: higher level functions for pcp groupsMake 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.
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.
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:
$ gap4
[... startup messages ...]
gap> LoadPackage("polycyclic");
true
gap>
Letâ€™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.
cd mygap
mkdir pkg
mv polycyclic.tar.gz pkg
cd pkg
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. 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.
$ gap4 -l ';mygap/'
[... startup messages ...]
gap> LoadPackage("polycyclic");
true
gap>