<p>Let <span class="SimpleMath">KG</span> be a group algebra of a finite <span class="SimpleMath">p</span>-group <span class="SimpleMath">G</span> over the field <span class="SimpleMath">K</span> of characteristic <span class="SimpleMath">p</span>, and let <span class="SimpleMath">V(KG)</span> be the normalized unit group of <span class="SimpleMath">KG</span>. The pc-presentation of the group <span class="SimpleMath">V(KG)</span> can be computed using the <strong class="pkg">GAP</strong> package <strong class="pkg">LAGUNA</strong> (<span class="URL"><a href="https://gap-packages.github.io/laguna/">https://gap-packages.github.io/laguna/</a></span>), 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 <span class="SimpleMath">p</span>-groups over the field of <span class="SimpleMath">p</span> elements. This allows the user to retrieve the pre-computed group from the library instead of the time-consuming 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 version <strong class="pkg">UnitLib</strong> 3.0.0 released in May 2009 also contained a parallel implementation of the computation of the normalized unit group of a modular group algebra of a finite <span class="SimpleMath">p</span>-group over the field of <span class="SimpleMath">p</span> elements, which works for groups from the <strong class="pkg">GAP</strong> small groups library. It is developed on the base of the sequential version of this algorithm (which works for any <span class="SimpleMath">p</span>-group with no limitations) from the <strong class="pkg">LAGUNA</strong> package. Parallelisation is implemented using the <strong class="pkg">SCSCP</strong> package that is capable of connecting several local or remote <strong class="pkg">GAP</strong> instances using the <strong class="pkg">SCSCP</strong> protocol.</p>
<p>In April 2012, <strong class="pkg">UnitLib</strong> 3.1.0 was updated to comply with <strong class="pkg">GAP</strong> 4.5.</p>
<p>The current version of <strong class="pkg">UnitLib</strong> provides the library of normalized unit groups <span class="SimpleMath">V(KG)</span> for all <span class="SimpleMath">p</span>-groups of order up to 243.</p>
<p>If you need to work with groups of bigger orders, please write to the maintainers, because they may be already computed or we can compute them for you.</p>
<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">[BKRS]</a>, we refer to the <a href="../../../pkg/laguna/doc/chap0.html#X7AA6C5737B711C89"><span class="RefLink">LAGUNA: LAGUNA package</span></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 <span class="SimpleMath">p</span>-group.</p>
<h4>1.3 <span class="Heading">Installation and system requirements</span></h4>
<p><strong class="pkg">UnitLib</strong> 5.0.0 requires at least <strong class="pkg">GAP</strong> 4.10. The libraries of normalized unit groups of groups of orders less than 243 are included in the distribution. The data for order 243 is available as an optional download.</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 <span class="URL"><a href="https://gap-packages.github.io/laguna/">https://gap-packages.github.io/laguna/</a></span>.</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 Lübeck and Max Neunhöffer, which is available from the <strong class="pkg">GAP</strong> homepage or from <span class="URL"><a href="http://www.math.rwth-aachen.de/~Frank.Luebeck/GAPDoc/">http://www.math.rwth-aachen.de/~Frank.Luebeck/GAPDoc/</a></span>.</p>
<p><strong class="pkg">UnitLib</strong> is distributed in standard formats (<code class="file">tar.gz</code>, <code class="file">tar.bz2</code>, <code class="file">.zip</code>, <code class="file">-win.zip</code>) and can be obtained from the <strong class="pkg">GAP</strong> homepage or from <span class="URL"><a href="https://gap-packages.github.io/unitlib/">https://gap-packages.github.io/unitlib/</a></span>. To install <strong class="pkg">UnitLib</strong>, unpack its archive into the <code class="file">pkg</code> subdirectory of your <strong class="pkg">GAP</strong> installation. When you don't have access to the directory of your main GAP installation, you can also install the package outside the GAP main directory by unpacking it inside a directory MYGAPDIR/pkg. Then to be able to load UnitLib you need to call GAP with the -l ";MYGAPDIR" option.
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