Introduction
General aims

Let KG be a group algebra of a finite p-group G over the field K of characteristic p, and let V(KG) be the normalized unit group of KG.

The pc-presentation of the group V(KG) can be computed using the &GAP; package &LAGUNA; (http://www.cs.st-andrews.ac.uk/˜alexk/laguna.htm), but for groups of orders 64 and more such computation will already take a lot of time.

The &UnitLib; package is an extension of the &LAGUNA; package that is focused on this problem. It contains the library of normalized unit groups of modular group algebras of finite p-groups over the field of p elements. This allows the user to retrieve the pre-computed group from the library instead of the long-time computation. The group created with &UnitLib; will have the same properties and attributes as the one computed with &LAGUNA;.

The current version of &UnitLib; provides the library of normalized unit groups V(KG) for all p-groups of order not greater than 243.

If you need to work with groups of bigger orders, please write to the authors, because we may already have them computed or can compute them for you.

Theoretical background

Since the &UnitLib; package is an extension of the &LAGUNA; package , we refer to the manual for the theoretical backround. In particular, Chapter 3 (The basic theory behind &LAGUNA;) of that manual contains definitions of the modular group algebra and its normalized unit group, the power-commutator presentation of the group, and also more details about the algorithm for the computation of the pc-presentation of the normalized unit group of a modular group algebra of a finite p-group.

Installation and system requirements

&UnitLib; is designed for &GAP;4.4 and no compatibility with previous releases of &GAP;4 is guaranteed.

Libraries of normalized unit groups of groups of orders less than 243, except for the order 128, will be available in any operating system.

The library for groups of order 128 was compressed using the gzip program and, therefore, will be available only in UNIX-type systems (including UNIX-installation in Mac OS X and Cygwin installation in Windows).

To work with the library for groups of order 243 you will also need the Curl program (http://curl.haxx.se) to retrieve the data from the UnitLib homepage, and the &GAP; package &QaoS; (http://www.gap-system.org/Packages/qaos.html) which provides the &GAP; function Curl to work with cURL.

If you need to work with groups of order 128 or 243 in Windows environment or you can not use Curl, please write to the authors. We will be able to give you a version of &UnitLib; with locally stored non-compressed data.

Because the &UnitLib; is an extension of the &LAGUNA; package, you must have the &LAGUNA; package installed. You can obtain it from the &GAP; homepage or from its homepage http://www.cs.st-andrews.ac.uk/˜alexk/laguna.htm.

To use the &UnitLib; online help it is necessary to install the &GAP;4 package &GAPDoc; by Frank L\"ubeck and Max Neunh\"offer, which is available from the &GAP; homepage or from http://www.math.rwth-aachen.de/˜Frank.Luebeck/GAPDoc/.

&UnitLib; is distributed in standard formats (zoo, tar.gz, tar.bz2, -win.zip) and can be obtained from the &GAP; homepage or from http://www.cs.st-andrews.ac.uk/˜alexk/unitlib.htm. To unpack the archive unitlib-2.1.zoo you need the program unzoo, which can be obtained from the &GAP; homepage http://www.gap-system.org/ (see section `Distribution'). To install &UnitLib;, copy this archive into the pkg subdirectory of your &GAP;4.4 installation. Then the subdirectory unitlib containing the package will be created in the pkg directory after the command

unzoo -x unitlib-2.1.zoo