# GAP 4 package Polycyclic

Authors: Bettina Eick, Max Horn, Werner Nickel
Needs: GAP, version 4.5 or more recent; GAP package Alnuth, version 1.0 or later; GAP package AutPGrp, version 1.4 or later
Current version: 2.11 (click here to see what's new)
Contact: Bettina Eick, Max Horn
Download: Several formats available

## Description

This package provides algorithms for working with polycyclic groups. 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, non-abelian the exterior square and the non-abelian tensor square

## (Bug) reports

If you use Polycyclic, we would like to know. A short email to one of us would be nice.

Any comments about the package are very welcome. If you have found important features missing or if there is a bug, let us know and we will try to address it as soon as possible.

## Installation

In order to install and use Polycyclic, your also need to install both Alnuth and AutPGrp. The former contains methods for algebraic number theory, the later for computations of automorphisms of p-groups; both are required by Polycyclic for various operations. The README file describes the installation of the Polycyclic package.

For the installation of Alnuth and AutPGrp, follow the instructions in their respective manuals.

## Online Documentation

The manual of Polycyclic is available as PDF and HTML.

If the package has been installed properly, the manual is also accessible through the GAP online help.

## Package Archive for Download

The Polycyclic package is availabe in the following formats:

- gzip compressed tar file
- bzip2 compressed tar file

The PackageInfo.g file is available as plain text file.