GAP (UnitLib) - Chapter 1: Introduction

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### 1. Introduction

#### 1.1 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://ukrgap.exponenta.ru/laguna.htm), but for groups of orders 64 and bigger this computation will already take a lot of time.

The UnitLib package is an extension of the LAGUNA package that is aimed 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.

#### 1.2 Installation and system requirements

UnitLib is designed for GAP4.4 and no compatibility with previous releases of GAP4 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 `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://ukrgap.exponenta.ru/laguna.htm.

To use the UnitLib online help it is necessary to install the GAP4 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 the GAP homepage or from http://homepages.vub.ac.be/~okonoval/unitlib.htm. To unpack the archive `unitlib-2.0.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 GAP4.4 installation. Then the subdirectory `unitlib` containing the package will be created in the `pkg` directory after the command `unzoo -x unitlib-2.0.zoo`

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