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<h1>nq</h1>
<h2>Nilpotent Quotients of Finitely Presented Groups</h2>
<p>
2.5.11</p>
<p>
12 January 2024
</p>
</div>
<p><b>
Werner Nickel
</b>
<br />Homepage: <span class="URL"><a href="http://www.mathematik.tu-darmstadt.de/~nickel/">http://www.mathematik.tu-darmstadt.de/~nickel/</a></span>
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<p><a id="X81488B807F2A1CF1" name="X81488B807F2A1CF1"></a></p>
<h3>Copyright</h3>
<p>© 1992-2007 Werner Nickel</p>
<p>The <strong class="pkg">nq</strong> package is free software; you can redistribute it and/or modify it under the terms of the <span class="URL"><a href="https://www.fsf.org/licenses/gpl.html">GNU General Public License</a></span> as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version.</p>
<p><a id="X82A988D47DFAFCFA" name="X82A988D47DFAFCFA"></a></p>
<h3>Acknowledgements</h3>
<p>The author of ANU NQ is Werner Nickel.</p>
<p>The development of this program was started while the author was supported by an Australian National University PhD scholarship and an Overseas Postgraduate Research Scholarship.</p>
<p>Further development of this program was done with support from the DFG-Schwerpunkt-Projekt "Algorithmische Zahlentheorie und Algebra".</p>
<p>Since then, maintenance of ANU NQ has been taken over by Max Horn. All credit for creating ANU NQ still goes to Werner Nickel as sole author. However, bug reports and other inquiries should be sent to Max Horn.</p>
<p>The following are the original acknowledgements by Werner Nickel.</p>
<p>Over the years a number of people have made useful suggestions that found their way into the code: Mike Newman, Michael Vaughan-Lee, Joachim Neubüser, Charles Sims.</p>
<p>Thanks to Volkmar Felsch and Joachim Neubüser for their careful examination of the package prior to its release for GAP 4.</p>
<p>This documentation was prepared with the <strong class="pkg">GAPDoc</strong> package by Frank Lübeck and Max Neunhöffer.</p>
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<h3>Contents<a id="contents" name="contents"></a></h3>
<div class="ContChap"><a href="chap1_mj.html#X7DFB63A97E67C0A1">1 <span class="Heading">Introduction</span></a>
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<div class="ContChap"><a href="chap2_mj.html#X7A696C2A78E88D1A">2 <span class="Heading">General remarks</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2_mj.html#X7E33A61A831C0068">2.1 <span class="Heading">Commutators and the Lower Central Series</span></a>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2_mj.html#X8463EF6A821FFB69">2.2 <span class="Heading">Nilpotent groups</span></a>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2_mj.html#X8268F8197E6BD786">2.3 <span class="Heading">Nilpotent presentations </span></a>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2_mj.html#X7DAF9CC17F6B868D">2.4 <span class="Heading">A sketch of the algorithm</span></a>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2_mj.html#X84EF796487BC1822">2.5 <span class="Heading">Identical Relations</span></a>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2_mj.html#X861A2C6385F6BCF5">2.6 <span class="Heading">Expression Trees</span></a>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2_mj.html#X7E27CA7F7E797520">2.7 <span class="Heading">A word about the implementation</span></a>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2_mj.html#X79E150AA823439A8">2.8 <span class="Heading">The input format of the standalone</span></a>
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<div class="ContChap"><a href="chap3_mj.html#X82738C527E6AC670">3 <span class="Heading">The Functions of the Package</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3_mj.html#X7D147D4182F85244">3.1 <span class="Heading">Nilpotent Quotients of Finitely Presented Groups</span></a>
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<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3_mj.html#X8216791583DE512C">3.1-1 NilpotentQuotient</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3_mj.html#X7ACCB6267C187AB0">3.1-2 NilpotentEngelQuotient</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3_mj.html#X8758F663782AE655">3.1-3 NqEpimorphismNilpotentQuotient</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3_mj.html#X827C2D4F78C982FC">3.1-4 LowerCentralFactors</a></span>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3_mj.html#X861A2C6385F6BCF5">3.2 <span class="Heading">Expression Trees</span></a>
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<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3_mj.html#X7CC7CDDD876BB8EB">3.2-1 ExpressionTrees</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3_mj.html#X879956307B67A136">3.2-2 EvaluateExpTree</a></span>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3_mj.html#X866E18057EF83F65">3.3 <span class="Heading">Auxiliary Functions</span></a>
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<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3_mj.html#X855407657CB86F40">3.3-1 NqReadOutput</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3_mj.html#X8443537679BC81D5">3.3-2 NqStringFpGroup</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3_mj.html#X82684F4D79A786F5">3.3-3 NqStringExpTrees</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3_mj.html#X7A28800579A2BB35">3.3-4 NqElementaryDivisors</a></span>
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<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3_mj.html#X87691A167A83FAF6">3.4-1 NqRuntime</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3_mj.html#X7DFBFD1580BF024A">3.4-2 NqDefaultOptions</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3_mj.html#X83D1AFCB7EFF4380">3.4-3 NqGlobalVariables</a></span>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3_mj.html#X804DD7CE815D87C9">3.5 <span class="Heading">Diagnostic Output</span></a>
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<div class="ContChap"><a href="chap4_mj.html#X7A489A5D79DA9E5C">4 <span class="Heading">Examples</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4_mj.html#X8638E6CE7B5955FB">4.1 <span class="Heading">Right Engel elements</span></a>
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<div class="ContChap"><a href="chap5_mj.html#X79E1ED167D631DCC">5 <span class="Heading">Installation of the Package</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5_mj.html#X783433687E4C822A">5.1 <span class="Heading">Configuring for compilation</span></a>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5_mj.html#X83FF596582258A74">5.2 <span class="Heading">Compiling the nq binary</span></a>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5_mj.html#X7DE7E7187BE24368">5.3 <span class="Heading">Testing</span></a>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5_mj.html#X80D704CC7EBFDF7A">5.4 <span class="Heading">Feedback</span></a>
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<div class="ContChap"><a href="chapA_mj.html#X78A212947932A6D3">A <span class="Heading">The nq command line interface</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chapA_mj.html#X7B495102781E821B">A.1 <span class="Heading">How to use the ANU NQ</span></a>
</span>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chapA_mj.html#X791091ED814A9B87">A.2 <span class="Heading">The input format for presentations</span></a>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chapA_mj.html#X7B5623E3821CC0D0">A.3 <span class="Heading">An example</span></a>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chapA_mj.html#X829490077E75F283">A.4 <span class="Heading">Some remarks about the algorithm</span></a>
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<div class="ContChap"><a href="chapBib_mj.html"><span class="Heading">References</span></a></div>
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