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<h3>1. Introduction</h3>

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<h4>1.1 General aims</h4>

<p>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 <strong class="pkg">GAP</strong> package <strong class="pkg">LAGUNA</strong> (<a href="http://www.cs.st-andrews.ac.uk/~alexk/laguna.htm">http://www.cs.st-andrews.ac.uk/~alexk/laguna.htm</a>), but for groups of orders 64 and more such computation will already take a lot of time.</p>

<p>The <strong class="pkg">UnitLib</strong> package is an extension of the <strong class="pkg">LAGUNA</strong> 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 <strong class="pkg">UnitLib</strong> will have the same properties and attributes as the one computed with <strong class="pkg">LAGUNA</strong>.</p>

<p>The current version of <strong class="pkg">UnitLib</strong> 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.</p>

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<h4>1.2 Theoretical background</h4>

<p>Since the <strong class="pkg">UnitLib</strong> package is an extension of the <strong class="pkg">LAGUNA</strong> package <a href="chapBib.html#biBLaguna">[BK+]</a>, we refer to the <a href="/Users/ericjespers/gap4r4/pkg/laguna/doc/chap0.html#s0ss1"><b>LAGUNA: LAGUNA package</b></a> manual for the theoretical backround. In particular, Chapter 3 (The basic theory behind <strong class="pkg">LAGUNA</strong>) 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.</p>

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<h4>1.3 Installation and system requirements</h4>

<p><strong class="pkg">UnitLib</strong> is designed for <strong class="pkg">GAP</strong>4.4 and no compatibility with previous releases of <strong class="pkg">GAP</strong>4 is guaranteed.</p>

<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>

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

<p>To work with the library for groups of order 243 you will also need the <code class="file">Curl</code> program (<a href="http://curl.haxx.se">http://curl.haxx.se</a>) to retrieve the data from the UnitLib homepage, and the <strong class="pkg">GAP</strong> package <strong class="pkg">Qaos</strong> (<a href="http://www.gap-system.org/Packages/qaos.html">http://www.gap-system.org/Packages/qaos.html</a>) which provides the <strong class="pkg">GAP</strong> function <code class="code">Curl</code> to work with <code class="file">cURL</code>.</p>

<p>If you need to work with groups of order 128 or 243 in Windows environment or you can not use <code class="file">Curl</code>, please write to the authors. We will be able to give you a version of <strong class="pkg">UnitLib</strong> with locally stored non-compressed data.</p>

<p>Because the <strong class="pkg">UnitLib</strong> is an extension of the <strong class="pkg">LAGUNA</strong> package, you must have the <strong class="pkg">LAGUNA</strong> package installed. You can obtain it from the <strong class="pkg">GAP</strong> homepage or from its homepage <a href="http://www.cs.st-andrews.ac.uk/~alexk/laguna.htm">http://www.cs.st-andrews.ac.uk/~alexk/laguna.htm</a>.</p>

<p>To use the <strong class="pkg">UnitLib</strong> online help it is necessary to install the <strong class="pkg">GAP</strong>4 package <strong class="pkg">GAPDoc</strong> by Frank L\"ubeck and Max Neunh\"offer, which is available from the <strong class="pkg">GAP</strong> homepage or from <a href="http://www.math.rwth-aachen.de/~Frank.Luebeck/GAPDoc/">http://www.math.rwth-aachen.de/~Frank.Luebeck/GAPDoc/</a>.</p>

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

<p><code class="code">unzoo -x unitlib-2.1.zoo</code></p>


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