# GAP 4 package Polycyclic

Authors: Bettina Eick, Werner Nickel
Needs: GAP, version 4.3 or more recent, GAP package Alnuth, version 1.0
Operating systems: UNIX
Current version: 2.2
Status:
Contact: Bettina Eick, Werner Nickel
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

You need to install both Polycyclic and Alnuth. The latter contains methods for algebraic number theory and an interface to the number theory system Kant. The README file describes the installation of the polycyclic package.

For the installation of Alnuth, follow the instructions in the Alnuth manual.

### Online Documentation

The manuals of Polycyclic and Alnuth are available in PostScript, PDF and HTML:

- Manual for Polycyclic: (Postscript) (PDF)
- Manual for Alnuth: (PDF) (HTML)

If the packages have been installed properly, these documents are also accessible through the GAP online help.

### Download

- the README file
- the PackageInfo.g file
- Polycyclic as gzipped tar archive (ca. 600k).
- Alnuth as gzipped tar archive (ca. 140k), as tar archive (ca. 370k)
- The Kant homepage