<!-- $Id: intro.xml,v 1.5 2007/03/14 20:41:57 alexk Exp $ -->
<Chapter Label="Intro">
<Heading>Introduction</Heading>    

<Section Label="Aims">
<Heading>General aims</Heading>

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

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

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 <M>p</M>-groups over the field
of <M>p</M> 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;.
<P/>

The current version of &UnitLib; provides the library of 
normalized unit groups <M>V(KG)</M> for all <M>p</M>-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.
<P/>

</Section>

<Section Label="TheoryUnitlib">
<Heading>Theoretical background</Heading>

Since the &UnitLib; package is an extension of the &LAGUNA; package 
<Cite Key="Laguna"/>, we refer to the 
<Ref Label="LAGUNA package" BookName="LAGUNA"/> 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 <M>p</M>-group.

</Section>


<Section Label="Install">
<Heading>Installation and system requirements</Heading>

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

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

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

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

If you need to work with groups of order 128 or 243 in Windows
environment or you can not use <File>Curl</File>, please write
to the authors. We will be able to give you a version of
&UnitLib; with locally stored non-compressed data. 
<P/>
 
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 
<URL>http://www.cs.st-andrews.ac.uk/&tilde;alexk/laguna.htm</URL>.
<P/>

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 
<URL>http://www.math.rwth-aachen.de/&tilde;Frank.Luebeck/GAPDoc/</URL>.
<P/> 

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

<C>unzoo -x unitlib-2.1.zoo</C>

</Section>

</Chapter>