<!-- $Id: intro.xml,v 1.7 2009/05/31 21:50:11 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 version &UnitLib; 3.0.0 released in May 2009 also contains a parallel 
implementation of the computation of the normalized unit group of a modular
group algebra of a finite <M>p</M>-group over the field of <M>p</M> elements,
which works for groups from the &GAP; small groups library. It is developed
on the base of the sequential version of this algorithm (which works for
any <M>p</M>-group with no limitations) from the &LAGUNA; package. 
Parallelisation is implemented using the &SCSCP; package that is capable of
connecting several local or remote &GAP; instances using the &SCSCP; protocol.
<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. 
<P/>
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-X.X.X.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-X.X.X.zoo</C>

</Section>

</Chapter>